

A130457


Triangle, read by rows of 3n+1 terms, where row n+1 is generated by taking partial sums of row n and then appending 2 zeros followed by the final term in the partial sums of row n, for n>=0, with T(0,0)=1.


1



1, 1, 0, 0, 1, 1, 1, 1, 2, 0, 0, 2, 1, 2, 3, 5, 5, 5, 7, 0, 0, 7, 1, 3, 6, 11, 16, 21, 28, 28, 28, 35, 0, 0, 35, 1, 4, 10, 21, 37, 58, 86, 114, 142, 177, 177, 177, 212, 0, 0, 212, 1, 5, 15, 36, 73, 131, 217, 331, 473, 650, 827, 1004, 1216, 1216, 1216, 1428, 0, 0, 1428, 1, 6, 21, 57
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OFFSET

0,9


LINKS

Table of n, a(n) for n=0..73.


EXAMPLE

Triangle begins:
.1;
.1, 0, 0, 1;
.1, 1, 1, 2, 0, 0, 2;
.1, 2, 3, 5, 5, 5, 7, 0, 0, 7;
.1, 3, 6, 11, 16, 21, 28, 28, 28, 35, 0, 0, 35;
.1, 4, 10, 21, 37, 58, 86, 114, 142, 177, 177, 177, 212, 0, 0, 212;
.1, 5, 15, 36, 73, 131, 217, 331, 473, 650, 827, 1004, 1216, 1216, 1216, 1428, 0, 0, 1428; ...


PROG

(PARI) {T(n, k)=local(A=[1], B); if(n==0, if(k==0, 1, 0), for(j=1, n, B=Vec(Ser(A)/(1x)); A=concat(concat(B, [0, 0]), B[ #B])); A[k+1])}


CROSSREFS

Cf. A130458 (final term in rows); A130456 (variant).
Sequence in context: A280912 A029303 A241067 * A130454 A070787 A033985
Adjacent sequences: A130454 A130455 A130456 * A130458 A130459 A130460


KEYWORD

nonn,tabf


AUTHOR

Paul D. Hanna, May 26 2007


STATUS

approved



