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Search: id:A104509
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| A104509 |
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Matrix inverse of triangle A104505, which is the right-hand side of triangle A084610 of coefficients in (1+x-x^2)^n. |
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+0
3
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| 1, 1, -1, 3, -2, 1, 4, -6, 3, -1, 7, -12, 10, -4, 1, 11, -25, 25, -15, 5, -1, 18, -48, 60, -44, 21, -6, 1, 29, -91, 133, -119, 70, -28, 7, -1, 47, -168, 284, -296, 210, -104, 36, -8, 1, 76, -306, 585, -699, 576, -342, 147, -45, 9, -1, 123, -550, 1175, -1580, 1485, -1022, 525, -200, 55, -10, 1, 199, -979, 2310, -3454, 3641
(list; table; graph; listen)
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OFFSET
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0,4
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COMMENT
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Left-most column is A000204 (Lucas numbers). Other columns include: A045925, A067988. Row sums are: {1,0,2,0,2,0,2,...}. Absolute row sums form: A099425. Antidiagonal sums are: {1,1,2,2,2,2,2,...}. Absolute antidiagonal sums are: A084214.
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FORMULA
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G.f.: A(x, y) = (1 + x^2)/(1-x-x^2 + x*y).
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EXAMPLE
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Rows begin:
1;
1,-1;
3,-2,1;
4,-6,3,-1;
7,-12,10,-4,1;
11,-25,25,-15,5,-1;
18,-48,60,-44,21,-6,1;
29,-91,133,-119,70,-28,7,-1;
47,-168,284,-296,210,-104,36,-8,1;
76,-306,585,-699,576,-342,147,-45,9,-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 + X^2)/(1-X-X^2 + X*Y), n, x), k, y)}
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CROSSREFS
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Cf. A104505, A000204.
Sequence in context: A077427 A107641 A127671 this_sequence A117212 A105033 A092486
Adjacent sequences: A104506 A104507 A104508 this_sequence A104510 A104511 A104512
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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), Mar 11 2005
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