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Search: id:A132784
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| A132784 |
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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. |
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+0
3
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| 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
(list; table; graph; listen)
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OFFSET
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0,12
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COMMENT
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Main diagonal (A132785) also yields (with offset) the row sums and the right-most border of this triangle.
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EXAMPLE
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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].
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PROGRAM
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(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])}
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CROSSREFS
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Cf. A132785 (main diagonal), A132786 (column sums).
Sequence in context: A049337 A076953 A093315 this_sequence A133873 A028953 A037865
Adjacent sequences: A132781 A132782 A132783 this_sequence A132785 A132786 A132787
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KEYWORD
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nonn,tabl
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Aug 29 2007
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