A236311 Riordan array ((1-x)/(1-3*x+3*x^2), x/(1-3*x+3*x^2)).

1, 2, 1, 3, 5, 1, 3, 15, 8, 1, 0, 33, 36, 11, 1, -9, 54, 117, 66, 14, 1, -27, 54, 297, 282, 105, 17, 1, -54, -27, 594, 945, 555, 153, 20, 1, -81, -297, 864, 2583, 2295, 963, 210, 23, 1, -81, -891, 513, 5778, 7803, 4725, 1533, 276, 26, 1, 0, -1863, -1944, 10098

Offset

0,2

Comments

Row sums are 3^n = A000244(n).

Diagonals sums are 2^n = A000079(n).

T(n,n) = A000012(n).

T(n+1,n) = A016789(n).

T(n+2,n) = A062741(n+1).

T(n+3,n) = 3*A004188(n+1).

T(n,0) = A057682(n+1).

Links

Table of n, a(n) for n=0..58.

Formula

T(n,k) = 3*T(n-1,k) + T(n-1,k-1) -3*T(n-2,k), T(0,0) = T(1,1) = 1, T(1,0) = 2, T(n,k) = 0 if k<0 or if k>n.

Example

Triangle begins :
1;
2, 1;
3, 5, 1;
3, 15, 8, 1;
0, 33, 36, 11, 1;
-9, 54, 117, 66, 14, 1;
-27, 54, 297, 282, 105, 17, 1;

Crossrefs

Cf. A057083, A057682, A000012, A016789, A062741

Sequence in context: A284429 A062105 A210563 * A347773 A368563 A093412

Adjacent sequences: A236308 A236309 A236310 * A236312 A236313 A236314

Keyword

easy,sign,tabl

Author

Philippe Deléham, Jan 21 2014

Status

approved