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A123149 Triangle T(n,k), 0<=k<=n, read by rows given by [1, 0, -1, 0, 0, 0, 0, 0, ...] DELTA [0, 1, 0, -1, 0, 0, 0, 0, ...] where DELTA is the operator defined in A084938. 2
1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 2, 2, 1, 0, 1, 2, 3, 2, 1, 0, 1, 3, 5, 5, 3, 1, 0, 1, 3, 6, 7, 6, 3, 1, 0, 1, 4, 9, 13, 13, 9, 4, 1, 0, 1, 4, 10, 16, 19, 16, 10, 4, 1, 0, 1, 5, 14, 26, 35, 35, 26, 14, 5, 1, 0, 1, 5, 15, 30, 45, 51, 45, 30, 15, 5, 1, 0, 1, 6, 20, 45, 75, 96, 96, 75, 45, 20, 6, 1, 0, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,12

COMMENTS

Row sums are A182522(n). - Philippe Deléham, May 04 2012

A169623 is a very similar triangle except it does not have the outer diagonal of 0's. - N. J. A. Sloane, Nov 23 2017

LINKS

Table of n, a(n) for n=0..91.

FORMULA

T(n,k)=T(n,n-1-k) . Sum_{k, 0<=k<=n}T(n,k)=A038754(n-1), for n>=1 . T(2*n,n)=A005773(n) . T(2*n+1,n)=A002426(n) . T(n,k)=T(n-1,k-1)+T(n-1,k)if n even, T(n,k)=T(n-1,k-1)+T(n-2,k)if n odd, T(0,0)=1, T(1,0)=1, T(1,1)=0, T(n,k)=0 if k<0 or if k>n.

G.f.: (1+x-y^2*x^2)/(1-x^2-y*x^2-y^2*x^2). - Philippe Deléham, May 04 2012

T(n,k) = T(n-2,k) + T(n-2,k-1) + T(n-2,k-2), T(0,0) = T(1,0) = T(2,0) = T(2,1) = 1, T(1,1) = T(2,2) = 0 and T(n,k) = 0 if k < 0 or if k > n. - Philippe Deléham, May 04 2012

EXAMPLE

Triangle begins:

1;

1, 0;

1, 1, 0;

1, 1, 1, 0;

1, 2, 2, 1, 0;

1, 2, 3, 2, 1, 0;

1, 3, 5, 5, 3, 1, 0;

1, 3, 6, 7, 6, 3, 1, 0;

1, 4, 9, 13, 13, 9, 4, 1, 0;

CROSSREFS

Cf. A027907, A169623, A182522, A169623.

Sequence in context: A194527 A104244 A116403 * A185158 A185700 A061926

Adjacent sequences:  A123146 A123147 A123148 * A123150 A123151 A123152

KEYWORD

nonn,tabl

AUTHOR

Philippe Deléham, Nov 05 2006

STATUS

approved

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Last modified November 17 23:26 EST 2019. Contains 329242 sequences. (Running on oeis4.)