A238156 Triangle T(n,k), 0<=k<=n, read by rows, given by (0, 1, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (2, -1/2, 1/2, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.

1, 0, 2, 0, 2, 3, 0, 2, 7, 4, 0, 2, 11, 16, 5, 0, 2, 15, 36, 30, 6, 0, 2, 19, 64, 91, 50, 7, 0, 2, 23, 100, 204, 196, 77, 8, 0, 2, 27, 144, 385, 540, 378, 112, 9, 0, 2, 31, 196, 650, 1210, 1254, 672, 156, 10, 0, 2, 35, 256, 1015, 2366, 3289, 2640, 1122, 210, 11

Offset

0,3

Comments

Row sums are A001519(n+1) = A122367(n).

Diagonal sums are A052969(n).

Links

Table of n, a(n) for n=0..65.

Formula

G.f.: (1-x)/(1-x-2*x*y+x^2*y^2).

Sum_{k=0..n} T(n,k)*2^k = 4^n = A000302(n).

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

Example

Triangle begins:
1;
0, 2;
0, 2, 3;
0, 2, 7, 4;
0, 2, 11, 16, 5;
0, 2, 15, 36, 30, 6;
0, 2, 19, 64, 91, 50, 7;
0, 2, 23, 100, 204, 196, 77, 8;
0, 2, 27, 144, 385, 540, 278, 112, 9;
0, 2, 31, 196, 650, 1210, 1254, 672, 156, 10;
0, 2, 35, 256, 1015, 2366, 3289, 2640, 1122, 210, 11;
...

Crossrefs

Cf. A016742, A004767, A005581, A005583

Sequence in context: A198061 A265583 A339754 * A281260 A182406 A160706

Adjacent sequences: A238153 A238154 A238155 * A238157 A238158 A238159

Keyword

nonn,tabl

Author

Philippe Deléham, Feb 18 2014

Status

approved