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Search: id:A113287
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| A113287 |
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Triangle T, read by rows, where row n of T equals row n of matrix (n+1)-th power of triangle A112555. |
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+0
6
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| 1, 2, 1, -3, 0, 1, 4, 4, 4, 1, -5, -10, -10, 0, 1, 6, 18, 24, 12, 6, 1, -7, -28, -49, -42, -21, 0, 1, 8, 40, 88, 104, 72, 24, 8, 1, -9, -54, -144, -216, -198, -108, -36, 0, 1, 10, 70, 220, 400, 460, 340, 160, 40, 10, 1, -11, -88, -319, -682, -946, -880, -550, -220, -55, 0, 1
(list; table; graph; listen)
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OFFSET
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0,2
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COMMENT
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Remarkably, the matrix logarithm (A113290) is an integer triangle. Matrix m-th power of A112555 = I + m*(A112555 - I) where I = identity matrix.
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FORMULA
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G.f.: A(x, y) = 1/(1-x*y) + x*(x+2)/((1-x*y)^2*(1+x+x*y)^2).
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EXAMPLE
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Triangle begins:
1;
2,1;
-3,0,1;
4,4,4,1;
-5,-10,-10,0,1;
6,18,24,12,6,1;
-7,-28,-49,-42,-21,0,1;
8,40,88,104,72,24,8,1;
-9,-54,-144,-216,-198,-108,-36,0,1;
10,70,220,400,460,340,160,40,10,1; ...
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PROGRAM
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(PARI) {T(n, k)=local(x=X+X*O(X^n), y=Y+Y*O(Y^k)); polcoeff(polcoeff(1/(1-x*y)+x*(x+2)/((1-x*y)^2*(1+x+x*y)^2), n, X), k, Y)}
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CROSSREFS
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Cf. A112555, A113288 (inverse), A113290 (log), A113291, A072374.
Adjacent sequences: A113284 A113285 A113286 this_sequence A113288 A113289 A113290
Sequence in context: A143239 A126988 A130026 this_sequence A096798 A137587 A137639
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KEYWORD
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sign,tabl
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Oct 23 2005
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