A132784 Triangle, read by rows of n*(n+1)/2 + 1 terms, where row n begins with n zeros followed by reverse partial sums of the prior row.

1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 2, 2, 2, 0, 0, 0, 0, 2, 4, 6, 7, 7, 7, 7, 0, 0, 0, 0, 0, 7, 14, 21, 28, 34, 38, 40, 40, 40, 40, 40, 0, 0, 0, 0, 0, 0, 40, 80, 120, 160, 200, 238, 272, 300, 321, 335, 342, 342, 342, 342, 342, 342, 0, 0, 0, 0, 0, 0, 0, 342, 684, 1026, 1368, 1710, 2052, 2387

Offset

0,12

Comments

Main diagonal (A132785) also yields (with offset) the row sums and the rightmost border of this triangle.

Links

Table of n, a(n) for n=0..76.

Example

Triangle begins:
1;
0, 1;
0,0, 1,1;
0,0,0, 1,2,2,2;
0,0,0,0, 2,4,6,7,7,7,7;
0,0,0,0,0, 7,14,21,28,34,38,40,40,40,40,40;
0,0,0,0,0,0, 40,80,120,160,200,238,272,300,321,335,342,342,342,342,342,342; ...
To obtain row 4 from row 3: [0,0,0, 1,2,2,2], start with 4 zeros followed by the partial sums of the reverse of row 3: partial_sums([2,2,2,1, 0,0,0]) = [2,4,6,7, 7,7,7].

Prog

(PARI) {T(n, k)=local(A=[1]); if(n==0, 1, for(i=1, n, B=Vec(Pol(A)/(1-x +x*O(x^(i*(i-1)/2)))); A=concat(vector(i), B)); A[k+1])}

Crossrefs

Cf. A132785 (main diagonal), A132786 (column sums).

Sequence in context: A093315 A204267 A237452 * A180834 A214458 A133873

Adjacent sequences: A132781 A132782 A132783 * A132785 A132786 A132787

Keyword

nonn,tabf

Author

Paul D. Hanna, Aug 29 2007

Status

approved