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A133569 A133566 * A007318 as infinite lower triangular matrices. 1
1, 1, 1, 2, 3, 1, 1, 3, 3, 1, 2, 7, 9, 5, 1, 1, 5, 10, 10, 5, 1, 2, 11, 25, 30, 20, 7, 1, 1, 7, 21, 35, 35, 21, 7, 1, 2, 15, 49, 91, 105, 77, 35, 9, 1, 1, 9, 36, 84, 126, 126, 84, 36, 9, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Row sums = A122756: (1, 2, 6, 8, 24, 32, 96,...).

With offset (0,4); triangle T(n,k), 0<=k<=n, given by [1,1,-3,1,0,0,0,0,0,0,0,...] DELTA [1,0,-2,1,0,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938 . - Philippe Deléham, Dec 15 2007

LINKS

Table of n, a(n) for n=1..55.

FORMULA

T(n,k) = T(n-2,k) + 2*T(n-2,k-1) + T(n-2,k-2), T(0,0) = 1, T(1,0) = T(1,1) = 1, T(2,0) = 2, T(2,1) = 3, T(2,2) = 1, T(n,k) = 0 if k<0 or if k>n. - Philippe Deléham, Sep 17 2014

G.f.: (-1-x-x*y-x^2-x^2*y)/((x*y+1+x)*(-1+x+x*y)). - R. J. Mathar, Aug 12 2015

EXAMPLE

First few rows of the triangle are:

1;

1, 1;

2, 3, 1;

1, 3, 3, 1;

2, 7, 9, 5, 1;

1, 5, 10, 10, 5, 1;

2, 11, 25, 30, 20, 7, 1;

1, 7, 21, 35, 35, 21, 7, 1;

...

CROSSREFS

Cf. A133566, A122756.

Sequence in context: A282290 A178795 A123185 * A141071 A004648 A265848

Adjacent sequences:  A133566 A133567 A133568 * A133570 A133571 A133572

KEYWORD

nonn,tabl

AUTHOR

Gary W. Adamson, Sep 16 2007

STATUS

approved

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Last modified October 21 06:03 EDT 2018. Contains 316405 sequences. (Running on oeis4.)