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A104587
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Triangle read by rows, given by the matrix product A * B where A (A094727) = [1; 2, 3; 3, 4, 5; 4, 5, 6, 7; ...] and B = [1; 1, 1; 1, 1, 1; ...] (both are infinite lower triangular matrices with the other terms zero).
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0
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1, 5, 3, 12, 9, 5, 22, 18, 13, 7, 35, 30, 24, 17, 9, 51, 45, 38, 30, 21, 11, 70, 63, 55, 46, 36, 25, 13, 92, 84, 75, 65, 54, 42, 29, 15, 117, 108, 98, 87, 75, 62, 48, 33, 17, 145, 135, 124, 112, 99, 85, 70, 54, 37, 19, 176, 165, 153, 140, 126, 111, 95, 78, 60, 41, 21
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OFFSET
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0,2
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COMMENTS
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Left column of the triangle = pentagonal numbers, A000326 (starting with 1).
Row sums = heptagonal pyramidal numbers, A002413.
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LINKS
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EXAMPLE
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Triangle begins:
1;
5, 3;
12, 9, 5;
22, 18, 13, 7;
35, 30, 24, 17, 9;
51, 45, 38, 30, 21, 11;
70, 63, 55, 46, 36, 25, 13;
92, 84, 75, 65, 54, 42, 29, 15;
...
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PROG
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(PARI) tabl(nn) = {ma = matrix(nn, nn, n, k, (n+k-1)*(k<=n)); mb = matrix(nn, nn, n, k, (k<=n)); mt = ma*mb; for (i=1, nn, for (j=1, i, print1(ma[i, j], ", "); ); print(); ); } \\ Michel Marcus, Mar 03 2014
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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