A238160 A skewed version of triangular array A029653.

1, 0, 2, 0, 1, 2, 0, 0, 3, 2, 0, 0, 1, 5, 2, 0, 0, 0, 4, 7, 2, 0, 0, 0, 1, 9, 9, 2, 0, 0, 0, 0, 5, 16, 11, 2, 0, 0, 0, 0, 1, 14, 25, 13, 2, 0, 0, 0, 0, 0, 6, 30, 36, 15, 2, 0, 0, 0, 0, 0, 1, 20, 55, 49, 17, 2, 0, 0, 0, 0, 0, 0, 7, 50, 91, 64, 19, 2, 0, 0, 0, 0, 0

Offset

0,3

Comments

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

Row sums are Fib(n+2).

Column sums are A003945(k).

Diagonal sums are (-1)^(n+1)*A109266(n+1).

T(3*n,2*n) = A029651(n).

Links

Table of n, a(n) for n=0..82.

Formula

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

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

Sum_{k=0..n} T(n,k)*x^k = A000007(n), A000045(n+2), A026150(n+1), A108306(n), A164545(n), A188168(n+1) for x = 0, 1, 2, 3, 4, 5 respectively.

Example

Triangle begins:
1;
0, 2;
0, 1, 2;
0, 0, 3, 2;
0, 0, 1, 5, 2;
0, 0, 0, 4, 7, 2;
0, 0, 0, 1, 9, 9, 2;
0, 0, 0, 0, 5, 16, 11, 2;
0, 0, 0, 0, 1, 14, 25, 13, 2;
0, 0, 0, 0, 0, 6, 30, 36, 15, 2;
0, 0, 0, 0, 0, 1, 20, 55, 49, 17, 2;
0, 0, 0, 0, 0, 0, 7, 50, 91, 64, 19, 2;
...

Crossrefs

Cf. A029635, A029653, A178524.

Sequence in context: A058650 A112177 A115723 * A178524 A321731 A358135

Adjacent sequences: A238157 A238158 A238159 * A238161 A238162 A238163

Keyword

easy,nonn,tabl

Author

Philippe Deléham, Feb 18 2014

Status

approved