#Oracle SQL 11.2, 218 216 201 bytes#

WITH v(a,b,c,d,i)AS(SELECT 0,1,1,4,3 FROM DUAL UNION ALL SELECT b,c,d,3*c-a,i+1 FROM v WHERE i<:1)SELECT SIGN(LEVEL-1) FROM DUAL WHERE LEVEL-1<=:1 CONNECT BY LEVEL<4UNION ALL SELECT d FROM v WHERE:1>2;

Un-golfed

WITH v(a,b,c,d,i) AS 
(
  SELECT 0,1,1,4,3 FROM DUAL 
  UNION ALL 
  SELECT b,c,d,3*c-a,i+1 FROM v WHERE i<:1
)
SELECT SIGN(LEVEL-1) FROM DUAL WHERE LEVEL-1<=:1 CONNECT BY LEVEL<4
UNION ALL SELECT d FROM v WHERE:1>2;

I managed to gain a few bytes by using (abusing ?) the SIGN function to generate the first 3 elements of the sequence.

Oracle SQL 11.2, 218 216 201 bytes

WITH v(a,b,c,d,i)AS(SELECT 0,1,1,4,3 FROM DUAL UNION ALL SELECT b,c,d,3*c-a,i+1 FROM v WHERE i<:1)SELECT SIGN(LEVEL-1) FROM DUAL WHERE LEVEL-1<=:1 CONNECT BY LEVEL<4UNION ALL SELECT d FROM v WHERE:1>2;

Un-golfed

WITH v(a,b,c,d,i) AS 
(
  SELECT 0,1,1,4,3 FROM DUAL 
  UNION ALL 
  SELECT b,c,d,3*c-a,i+1 FROM v WHERE i<:1
)
SELECT SIGN(LEVEL-1) FROM DUAL WHERE LEVEL-1<=:1 CONNECT BY LEVEL<4
UNION ALL SELECT d FROM v WHERE:1>2;

I managed to gain a few bytes by using (abusing ?) the SIGN function to generate the first 3 elements of the sequence.

#Oracle SQL 11.2, 218 216 bytes#

WITH v(a,b,c,d,i)AS(SELECT 0,1,1,4,3 FROM DUAL UNION ALL SELECT b,c,d,3*c-a,i+1 FROM v WHERE i<:1)SELECT 0 FROM DUAL UNION ALL SELECT 1 FROM DUAL WHERE LEVEL<=:1 CONNECT BY LEVEL<3UNION ALL SELECT d FROM v WHERE:1>2;

Un-golfed

WITH v(a,b,c,d,i) AS
(
  SELECT 0,1,1,4,3 FROM DUAL
  UNION ALL
  SELECT b,c,d,3*c-a,i+1 FROM v WHERE i<:1 
)
SELECT 0 FROM DUAL
UNION ALL SELECT 1 FROM DUAL WHERE LEVEL<=:1 CONNECT BY LEVEL<3
UNION ALl SELECT d FROM v WHERE :1>2;

Still looking for a way to cut the SELECT 0... and SELECT 1... from the query.

#Oracle SQL 11.2, 218 216 201 bytes#

WITH v(a,b,c,d,i)AS(SELECT 0,1,1,4,3 FROM DUAL UNION ALL SELECT b,c,d,3*c-a,i+1 FROM v WHERE i<:1)SELECT SIGN(LEVEL-1) FROM DUAL WHERE LEVEL-1<=:1 CONNECT BY LEVEL<4UNION ALL SELECT d FROM v WHERE:1>2;

Un-golfed

WITH v(a,b,c,d,i) AS 
(
  SELECT 0,1,1,4,3 FROM DUAL 
  UNION ALL 
  SELECT b,c,d,3*c-a,i+1 FROM v WHERE i<:1
)
SELECT SIGN(LEVEL-1) FROM DUAL WHERE LEVEL-1<=:1 CONNECT BY LEVEL<4
UNION ALL SELECT d FROM v WHERE:1>2;

I managed to gain a few bytes by using (abusing ?) the SIGN function to generate the first 3 elements of the sequence.

#Oracle SQL 11.2, 218 bytes#

WITH v(a,b,c,d,i) AS(SELECT 0,1,1,4,3 FROM DUAL UNION ALL SELECT b,c,d,3*c-a,i+1 FROM v WHERE i<:1)SELECT 0 FROM DUAL UNION ALL SELECT 1 FROM DUAL WHERE LEVEL<=:1 CONNECT BY LEVEL<3UNION ALL SELECT d FROM v WHERE :1>2;

Un-golfed

WITH v(a,b,c,d,i) AS
(
  SELECT 0,1,1,4,3 FROM DUAL
  UNION ALL
  SELECT b,c,d,3*c-a,i+1 FROM v WHERE i<:1 
)
SELECT 0 FROM DUAL
UNION ALL SELECT 1 FROM DUAL WHERE LEVEL<=:1 CONNECT BY LEVEL<3
UNION ALl SELECT d FROM v WHERE :1>2;

Still looking for a way to cut the SELECT 0... and SELECT 1... from the query.

#Oracle SQL 11.2, 218 216 bytes#

WITH v(a,b,c,d,i)AS(SELECT 0,1,1,4,3 FROM DUAL UNION ALL SELECT b,c,d,3*c-a,i+1 FROM v WHERE i<:1)SELECT 0 FROM DUAL UNION ALL SELECT 1 FROM DUAL WHERE LEVEL<=:1 CONNECT BY LEVEL<3UNION ALL SELECT d FROM v WHERE:1>2;

Un-golfed

WITH v(a,b,c,d,i) AS
(
  SELECT 0,1,1,4,3 FROM DUAL
  UNION ALL
  SELECT b,c,d,3*c-a,i+1 FROM v WHERE i<:1 
)
SELECT 0 FROM DUAL
UNION ALL SELECT 1 FROM DUAL WHERE LEVEL<=:1 CONNECT BY LEVEL<3
UNION ALl SELECT d FROM v WHERE :1>2;

Still looking for a way to cut the SELECT 0... and SELECT 1... from the query.