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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 repectivelyrespectively.

Cf. A029635, A029653, A178524.

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proposed

reviewed

editing

proposed

allocated for Philippe Deléham

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

0,3

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).

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 repectively.

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;

...

Cf. A029635, A029653, A178524

allocated

easy,nonn,tabl

Philippe Deléham, Feb 18 2014

approved

editing

allocated for Philippe Deléham

allocated

approved