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A238160 A skewed version of triangular array A029653. 0
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 (list; table; graph; refs; listen; history; text; internal format)
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 A212357

Adjacent sequences:  A238157 A238158 A238159 * A238161 A238162 A238163

KEYWORD

easy,nonn,tabl

AUTHOR

Philippe Deléham, Feb 18 2014

STATUS

approved

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Last modified August 13 22:34 EDT 2020. Contains 336465 sequences. (Running on oeis4.)