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Search: id:A126465
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| A126465 |
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Triangle T, read by rows, where row n equals row (n-1) of matrix power T^(n(n+1)/2) concatenated with a trailing '1', for n>0, with T(0,0) = 1. |
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10
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| 1, 1, 1, 3, 1, 1, 33, 6, 1, 1, 855, 105, 10, 1, 1, 40475, 3710, 255, 15, 1, 1, 3039204, 219625, 11935, 525, 21, 1, 1, 331630320, 19545316, 879571, 31584, 966, 28, 1, 1, 49563943161, 2437990653, 93365328, 2856819, 72786, 1638, 36, 1, 1
(list; table; graph; listen)
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OFFSET
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0,4
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COMMENT
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Amazingly, A126465 = A126450*A126445^-1 = A126454*A126450^-1 = A126457*A126454^-1; and also A126460 = A126445^-1*A126450 = A126450^-1*A126454 = A126454^-1*A126457.
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EXAMPLE
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Triangle T begins:
1,
1, 1,
3, 1, 1,
33, 6, 1, 1,
855, 105, 10, 1, 1,
40475, 3710, 255, 15, 1, 1,
3039204, 219625, 11935, 525, 21, 1, 1,
331630320, 19545316, 879571, 31584, 966, 28, 1, 1,
49563943161, 2437990653, 93365328, 2856819, 72786, 1638, 36, 1, 1, ...
Matrix cube T^3 begins:
1;
[3, 1]; <-- row 1 of T^3 + '1' = row 2 of T;
12, 3, 1; ...
Matrix power T^6 begins:
1;
6, 1;
[33, 6, 1]; <-- row 2 of T^6 + '1' = row 3 of T.
Matrix power T^10 begins:
1;
10, 1;
75, 10, 1;
[855, 105, 10, 1]; <-- row 3 of T^10 + '1' = row 4 of T.
Matrix power T^15 begins:
1;
15, 1;
150, 15, 1;
1895, 195, 15, 1;
[40475, 3710, 255, 15, 1]; <-- row 4 of T^15 + '1' = row 5 of T.
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PROGRAM
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(PARI) {T(n, k)=local(M=matrix(n+1, n+1, r, c, if(r>=c, binomial((r-1)*r*(r+1)/3!-(c-1)*c*(c+1)/3!, r-c))), N=matrix(n+1, n+1, r, c, if(r>=c, binomial((r-1)*r*(r+1)/3!-(c-1)*c*(c+1)/3!+1, r-c)))); (N*M^-1)[n+1, k+1]}
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CROSSREFS
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Columns: A126466, A126467, A126468; A126469 (row sums); A126460 (dual); A101479 (variant).
Sequence in context: A111382 A156950 A083998 this_sequence A077509 A156698 A083993
Adjacent sequences: A126462 A126463 A126464 this_sequence A126466 A126467 A126468
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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), Dec 27 2006
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