J, 14 chars

This is just hardcoding the [1,2, 4+3*k (k=0..n-1) ] sequence and takes the first N.

   ({.1,2,4+3*i.) 10
1 2 4 7 10 13 16 19 22 25

. J, 18 chars

This one uses the linear combination of [0,1,2,3...], [1,1,0,0...] and [0,1,1,1...]. Should be shorter but can't seem to golf it.

   ((3&*+<&2-2**)@i.) 10
1 2 4 7 10 13 16 19 22 25

J, 14 chars

This just hardcodes the [1,2, 4+3*k (k=0..n-1) ] sequence and takes the first N.

   ({.1,2,4+3*i.) 10
1 2 4 7 10 13 16 19 22 25

. J, 18 chars

This one uses a linear combination of [0,1,2,3...], [1,1,0,0...] and [0,1,1,1...]. Should be shorter but can't seem to golf it.

   ((3&*+<&2-2**)@i.) 10
1 2 4 7 10 13 16 19 22 25

J, 14 chars

This is just hardcoding the [1,2, 4+3*k (k=0..n) ] sequence and takes the first N.

   ({.1,2,4+3*i.) 10
1 2 4 7 10 13 16 19 22 25

. J, 18 chars

This one uses the linear combination of [0,1,2,3...], [1,1,0,0...] and [0,1,1,1...]. Should be shorter but can't seem to golf it.

   ((3&*+<&2-2**)@i.) 10
1 2 4 7 10 13 16 19 22 25

J, 14 chars

This is just hardcoding the [1,2, 4+3*k (k=0..n-1) ] sequence and takes the first N.

   ({.1,2,4+3*i.) 10
1 2 4 7 10 13 16 19 22 25

. J, 18 chars

This one uses the linear combination of [0,1,2,3...], [1,1,0,0...] and [0,1,1,1...]. Should be shorter but can't seem to golf it.

   ((3&*+<&2-2**)@i.) 10
1 2 4 7 10 13 16 19 22 25

J, 18 chars

This should be shorter... trying to golf more.

   ((3&*+<&2-2**)@i.) 10
1 2 4 7 10 13 16 19 22 25

J, 14 chars

This is just hardcoding the [1,2, 4+3*k (k=0..n) ] sequence and takes the first N.

   ({.1,2,4+3*i.) 10
1 2 4 7 10 13 16 19 22 25

. J, 18 chars

This one uses the linear combination of [0,1,2,3...], [1,1,0,0...] and [0,1,1,1...]. Should be shorter but can't seem to golf it.

   ((3&*+<&2-2**)@i.) 10
1 2 4 7 10 13 16 19 22 25