



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
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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(n2,k) + 2*T(n2,k1) + T(n2,k2), 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.: (1xx*yx^2x^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



