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A110330
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Inverse of a number triangle related to the Pell numbers.
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5
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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; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| 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
| 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
| 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
| Sequence in context: A181302 A143446 A132014 * A097864 A097866 A097865
Adjacent sequences: A110327 A110328 A110329 * A110331 A110332 A110333
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KEYWORD
| easy,sign,tabl
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Jul 20 2005
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