A236420 Riordan array (1/(1-3*x), (1-3*x-sqrt(1-6*x+5*x^2))/(2*x)).

1, 3, 1, 9, 6, 1, 27, 28, 9, 1, 81, 120, 56, 12, 1, 243, 497, 300, 93, 15, 1, 729, 2034, 1490, 594, 139, 18, 1, 2187, 8321, 7098, 3411, 1029, 194, 21, 1, 6561, 34248, 33026, 18360, 6692, 1632, 258, 24, 1, 19683, 142331, 151686, 94798, 40068, 11846, 2430, 331, 27, 1

Offset

0,2

Comments

T(n,0) = 3^n = A000244(n).

T(n,2) = A002212(n+1) - 3^n.

T(n+1,n) = 3n+3 = A008585(n+1).

T(n+2,n) = (9*n^2+29*n+18)/2.

Links

Table of n, a(n) for n=0..54.

Formula

T(n,0) = 3*T(n-1,0), T(n,k) = T(n-1,k-1) + 3*T(n-1,k) + T(n-1,k+1) for k>0, T(n,k) = 0 if k<0 or if k>n, T(0,0) = 1.

Example

Triangle begins:
1;
3, 1;
9, 6, 1;
27, 28, 9, 1;
81, 120, 56, 12, 1;
243, 497, 300, 93, 15, 1;
729, 2034, 1490, 594, 139, 18, 1

Crossrefs

Cf. Similar sequences: A091965, A110165

Sequence in context: A178831 A027465 A164942 * A187537 A246256 A157393

Adjacent sequences: A236417 A236418 A236419 * A236421 A236422 A236423

Keyword

nonn,tabl

Author

Philippe Deléham, Jan 25 2014

Status

approved