0,5

Triangle T(n,k), 0<=k<=n, read by rows defined by : T(0,0)=1, T(n,k)=0 if k<0 or if k>n, T(n,0)=T(n-1,1), T(n,k)=T(n-1,k-1)+2*T(n-1,k)+T(n-1,k+1) for k>=1.

Diagonal sums are A065601 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Mar 05 2007

This triangle belongs to the family of triangles defined by: T(0,0)=1, T(n,k)=0 if k<0 or if k>n, T(n,0)=x*T(n-1,0)+T(n-1,1), T(n,k)=T(n-1,k-1)+y*T(n-1,k)+T(n-1,k+1) for k>=1 . Other triangles arise by choosing different values for (x,y): (0,0) -> A053121; (0,1) -> A089942; (0,2) -> A126093; (0,3) -> A126970; (1,0)-> A061554; (1,1) -> A064189; (1,2) -> A039599; (1,3) -> A110877; ((1,4) -> A124576; (2,0) -> A126075; (2,1) -> A038622; (2,2) -> A039598; (2,3) -> A124733; (2,4) -> A124575; (3,0) -> A126953; (3,1) -> A126954; (3,2) -> A111418; (3,3) -> A091965; (3,4) -> A124574; (4,3) -> A126791; (4,4) -> A052179; (4,5) -> A126331; (5,5) -> A125906 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Sep 25 2007

Sum_{k, 0<=k<=n}T(m,k)*T(n,k)=T(m+n,0)=A000957(m+n+1).

Sum[k, 0<=k<=n-1}A126093(n,k)=A026641(n), for n>=1 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Mar 05 2007

Sum_{k, 0<=k<=n}T(n,k)*(3k+1)=4^n . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Mar 22 2007

Triangle begins:

1;

0, 1;

1, 2, 1;

2, 6, 4, 1;

6, 18, 15, 6, 1;

18, 57, 54, 28, 8, 1;

57, 186, 193, 118, 45, 10, 1;

186, 622, 690, 474, 218, 66, 12, 1;

622, 2120, 2476, 1856, 976, 362, 91, 14, 1;

2120, 7338, 8928, 7164, 4170, 1791, 558, 120, 16, 1;

Sequence in context: A060550 A099206 A121341 this_sequence A065279 A151962 A072137

Adjacent sequences: A126090 A126091 A126092 this_sequence A126094 A126095 A126096

nonn,tabl

Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Mar 03 2007