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Search: id:A110330
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| A110330 |
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Inverse of a number triangle related to the Pell numbers. |
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+0
6
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| 1, -2, 1, -2, -4, 1, 0, -6, -6, 1, 0, 0, -12, -8, 1, 0, 0, 0, -20, -10, 1, 0, 0, 0, 0, -30, -12, 1, 0, 0, 0, 0, 0, -42, -14, 1, 0, 0, 0, 0, 0, 0, -56, -16, 1, 0, 0, 0, 0, 0, 0, 0, -72, -18, 1, 0, 0, 0, 0, 0, 0, 0, 0, -90, -20, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -110, -22, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -132, -24, 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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This is the matrix inverse of A110327.
Row sums are A110331. Diagonal sums are A110322. Inverse of A110327. The result can be generalized as follows: The triangle whose columns have e.g.f. (x^k/k!)/(1-a*x-b*x^2) has inverse T(n,k)=if(n=k,1,if(n-k=1,-a*binomial(n,1),if(n-k=2,-2*b*binomial(n,2),0))).
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FORMULA
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T(n, k)=if(n=k, 1, if(n-k=1, -2*binomial(n, 1), if(n-k=2, -2*binomial(n, 2), 0)))
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EXAMPLE
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Rows begin
1;
-2,1;
-2,-4,1;
0,-6,-6,1;
0,0,-12,-8,1;
0,0,0,-20,-10,1;
0,0,0,0,-30,-12,1;
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CROSSREFS
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Sequence in context: A137408 A007461 A132014 this_sequence A097864 A097866 A097865
Adjacent sequences: A110327 A110328 A110329 this_sequence A110331 A110332 A110333
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KEYWORD
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easy,sign,tabl
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Jul 20 2005
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