85
votes
Accepted
Extending OEIS: Counting Diamond Tilings
Algebra, graph theory, Möbius inversion, research, and Java
The symmetry group of the hexagon is the dihedral group of order 12, and is generated by a 60 degree rotation and a mirror flip across a ...
- 42.8k
51
votes
Absolute Sums of Sidi Polynomial Coefficients
Python 2, 43 bytes
f=lambda n,k=1:k/n or n*f(n,k+1)+k*f(n-1,k)
Try it online!
A different approach
Ever since I posted this challenge, I tried to come up with a ...
- 207k
34
votes
Print all colorings of a 3x3 grid
Mathematica, 25 bytes
Image/@{0,1}~Tuples~{3,3}
Gives an array with all the grids as images, which is also directly displayed on screen:
(Cropped so as not to ...
- 193k
34
votes
31
votes
Anaglot Polygrams
34 Languages, 19 bytes, Score: 38,832,018,459,912,437,760,000
Here is a quick answer I threw together to show that it is possible to get an answer scoring better than 1.
...
- 88.8k
28
votes
Every word from babab to zyzyz
Mathematica, 72 65 61 bytes
Print@@@Tuples@{a=##/(b=#5#9#15#21#25#)&@@Alphabet[],b,a,b,a}
For testing, I recommend replacing ...
- 193k
27
votes
Catalan Numbers
C, 78 52 39 34 33 bytes
Even more C magic (thanks xsot):
c(n){return!n?:(4+6./~n)*c(n-1);}
?: is a GNU extension.
This time ...
- 1,079
26
votes
Concentric rings on a snub square tiling
Ruby, 26 bytes
->n{~-n*12-496/4**n%4+1/n}
Try it online!
Revised version adding 1/n and subtracting ...
- 24.9k
25
votes
Bernoulli Numbers
Mathematica, 40 28 23 22 bytes
Using the famous formula n*ζ(1−n)=−Bn, where ζ is the Riemann Zeta function.
If[#>0,-Zeta[1-#]#,1]&
The same length:
<...
- 35k
25
votes
25
votes
The square root of the square root of the square root of the…
APL (Dyalog Unicode), 39 bytes
+/⊢{∨/⍺⍵<⍵0:0⋄⍺=0:1⋄+/∊∇¨/⍺(⍵*2)-⊂⍳⍺}¨⍳
Try it online!
A tacit function containing an inner dfn to use recursion. Does not use ...
- 62.9k
24
votes
23
votes
Compute the multinomial coefficient
Jelly, 7 6 bytes
;_/!:/
Look ma, no Unicode! This program takes a single list as input, with n at its first index.
Try it online! or verify all test cases at ...
- 207k
23
votes
Brute-force the switchboard
Haskell, 25 24 23 17 bytes
mapM$min"^v".pure
Try it online!
-1 byte thanks to @H.PWiz
-1 byte thanks to @nimi
Returns a list of strings. The TIO has 2 extra ...
- 3,916
21
votes
Don't repeat yourself in Rock-Paper-Scissors
Ruby, 39 bytes
->n{(?P*n..?S*n).grep_v /[^RPS]|(.+)\1/}
This hilariously inefficient function generates all strings of length N that lie alphabetically ...
- 21.8k
20
votes
Accepted
The Combinatorics of Transistor
CJam (56 bytes)
q~4@:Nm*:$_&{:+1$\-N),&},f{1$1$:+-\0-:(_e`0f=+++:m!:/}:+
Online demo
This is an optimised version of the reference implementation I ...
- 42.8k
20
votes
Count sums of two squares
Python (59 57 56 bytes)
lambda n:0**n+sum((-(n%(x-~x)<1))**x*4for x in range(n))
Online demo
As with my CJam answer, this uses Möbius inversion and runs in ...
- 42.8k
20
votes
Partitioning the grid into triangles
Haskell, 60 55 54 52 bytes
After a drawing and programming a lot of examples, it occured to me that this is the same as the problem of the rooks:
On a \$(n+1) \times (n+1)\$ chessboard, how many ...
- 43.1k
19
votes
Stuffing primes in a box
Smalltalk, 1098 primes
First off, nice hard question - as evidenced by the lack of non-trivial responses thus far.
I had a solution cooking at work, but had to wait for the long weekend to have time ...
19
votes
Deranged !Combinatorics: Compute the Subfactorial
Funciton, 336 bytes
Byte count assumes UTF-16 encoding with BOM.
...
- 193k
19
votes
Counting universal n-ary logic gates
Python 3.8 (pre-release), 287 282 242 bytes
-5 bytes thanks to @Dialfrost
...
- 6,705
18
votes
Combinatorial products of unique primes
Pure Bash, 32 bytes
eval echo \$[{1,${1// /\}*{1,}}]
Reads input list (single space separated) passed as a command-line arg.
Three different shell expansions are ...
- 69.2k
18
votes
A penny saved is a penny
Haskell, 37 34 bytes
s#l@(c:d)|s>=c=(s-c)#l+s#d
s#_=0^s
Usage example: 26 # [1,5,10,25] -> ...
- 35.3k
17
votes
Code-Golf: Permutations
Python, 52
Input is a set. Output is a list of lists.
f=lambda a:[p+[x]for x in a for p in f(a-{x})]or[[]]
This is shorter than the answer that does all the work ...
- 30.9k
17
votes
Accepted
Generate all combinations of given list of elements, sorted
Jelly, 1 byte
ṗ
TryItOnline
Cartesian power built-in atom, as a dyadic link with left argument the items and right argument the count, or as a full program with ...
- 92k
17
votes
17
votes
Enumerate all pure sets
Python, 43 bytes
f=lambda x:[f(i)for i in range(x)if x>>i&1]
Attempt This Online!
Outputs the \$ n \$th set, starting at \$ 0 \$.
One way of creating a sequence of all pure sets is to encode ...
- 21.5k
16
votes
Accepted
16
votes
Count sums of two squares
Python 2, 44 bytes
f=lambda n,x=1:+(x>n)or(n%x<1)-f(n,x+2)/4<<2
This is almost the same as xsot's solution (which is based on Peter Taylor's solution)...
- 5,799
16
votes
Super permutations
Scratch 3.0, 65 blocks / 637 632 bytes
Look at y'all, having fun with your fancy shmancy permutation functions/map tools. Well, not I! No, not I! When using Scratch, one has to do things themselves! ...
- 22.1k
Only top scored, non community-wiki answers of a minimum length are eligible