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 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,9 LINKS 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)/(1-x)); A=concat(concat(B, [0, 0]), B[ #B])); A[k+1])} CROSSREFS Cf. A130458 (final term in rows); A130456 (variant). Sequence in context: A281640 A281452 A241067 * A130454 A070787 A033985 Adjacent sequences:  A130454 A130455 A130456 * A130458 A130459 A130460 KEYWORD nonn,tabf AUTHOR Paul D. Hanna, May 26 2007 STATUS approved

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