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A077961
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Expansion of 1 / (1 + x^2 - x^3) in powers of x.
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4
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1, 0, -1, 1, 1, -2, 0, 3, -2, -3, 5, 1, -8, 4, 9, -12, -5, 21, -7, -26, 28, 19, -54, 9, 73, -63, -64, 136, 1, -200, 135, 201, -335, -66, 536, -269, -602, 805, 333, -1407, 472, 1740, -1879, -1268, 3619, -611, -4887, 4230, 4276, -9117, -46, 13393, -9071, -13439, 22464, 4368, -35903, 18096, 40271, -53999
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,6
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REFERENCES
| Hirschhorn, Michael D., Non-trivial intertwined second-order recurrence relations, Fibonacci Quart. 43 (2005), no. 4, 316-325. See L_n.
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FORMULA
| a(n)=sum{k=0..floor(n/2), binomial(k, n-2k)(-1)^(n-k)} - Paul Barry (pbarry(AT)wit.ie), Jun 24 2005
a(n) = term (1,1) in matrix [0,1,0; -1,0,1; 1,0,0]^n. a(n) = A000930 (-3-n). - Alois P. Heinz (heinz(AT)hs-heilbronn.de), Jun 20 2008
a(-n) = A078012(n). - Michael Somos May 03 2011
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EXAMPLE
| 1 - x^2 + x^3 + x^4 - 2*x^5 + 3*x^7 - 2*x^8 - 3*x^9 + 5*x^10 + x^11 + ...
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MAPLE
| a := n -> (Matrix([[0, 1, 0], [ -1, 0, 1], [1, 0, 0]])^n)[1, 1]; seq (a(n), n=0..50); - Alois P. Heinz (heinz(AT)hs-heilbronn.de), Jun 20 2008
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PROG
| (PARI) {a(n) = if( n<0, n = -n; polcoeff( (1 - x) / (1 - x - x^3) + x * O(x^n), n) , polcoeff( 1 / (1 + x^2 - x^3) + x * O(x^n), n))} /* Michael Somos May 03 2011 */
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CROSSREFS
| Cf. A000930, A078012.
Sequence in context: A051613 A173291 * A077962 A078031 A089196 A140944
Adjacent sequences: A077958 A077959 A077960 * A077962 A077963 A077964
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KEYWORD
| sign
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Nov 17 2002
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