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A183202
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Triangle, read by rows, where T(n,k) equals the sum of (n-k) terms in row n of triangle A131338 starting at position nk - k(k-1)/2, with the main diagonal formed from the row sums.
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2
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1, 1, 1, 2, 1, 2, 3, 3, 3, 5, 4, 6, 10, 9, 14, 5, 10, 22, 34, 29, 43, 6, 15, 40, 84, 122, 100, 143, 7, 21, 65, 169, 334, 463, 367, 510, 8, 28, 98, 300, 738, 1390, 1851, 1426, 1936, 9, 36, 140, 489, 1426, 3345, 6043, 7767, 5839, 7775, 10, 45, 192, 749, 2510, 6990, 15735
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history;
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OFFSET
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0,4
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LINKS
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EXAMPLE
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Triangle begins:
1;
1,1;
2,1,2;
3,3,3,5;
4,6,10,9,14;
5,10,22,34,29,43;
6,15,40,84,122,100,143;
7,21,65,169,334,463,367,510;
8,28,98,300,738,1390,1851,1426,1936;
9,36,140,489,1426,3345,6043,7767,5839,7775;
10,45,192,749,2510,6990,15735,27374,34097,25094,32869; ...
The rows are derived from triangle A131338 by summing terms in the following manner:
(1);
(1),(1);
(1+1),(1),(2);
(1+1+1),(1+2),(3),(5);
(1+1+1+1),(1+2+3),(4+6),(9),(14);
(1+1+1+1+1),(1+2+3+4),(5+7+10),(14+20),(29),(43);
(1+1+1+1+1+1),(1+2+3+4+5),(6+8+11+15),(20+27+37),(51+71),(100),(143); ...
where row n of triangle A131338 consists of n '1's followed by the partial sums of the prior row.
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PROG
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(PARI) {A131338(n, k)=if(k>n*(n+1)/2|k<0, 0, if(k<=n, 1, sum(i=0, k-n, A131338(n-1, i))))}
{T(n, k)=if(n==k, A131338(n, n*(n+1)/2), sum(j=n*k-k*(k-1)/2, n*k-k*(k-1)/2+n-k-1, A131338(n, j)))}
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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