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A071100
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Expansion of (5 + 3*x + x^2 - x^3) / (1 - 2*x - 2*x^2 - 2*x^3 + x^4) in powers of x.
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3
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5, 13, 37, 109, 313, 905, 2617, 7561, 21853, 63157, 182525, 527509, 1524529, 4405969, 12733489, 36800465, 106355317, 307372573, 888323221, 2567301757, 7419639785, 21443156953, 61971873769, 179102039257, 517614500173, 1495933669445, 4323328543981
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| Number of tilings of the 0-mod-4 pillow of order n is a perfect square times a(n). [Propp, 1999, p. 271]
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REFERENCES
| J. Propp, Enumeration of matchings: problems and progress, pp. 255-291 in L. J. Billera et al., eds, New Perspectives in Algebraic Combinatorics, Cambridge, 1999 (see Problem 12).
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LINKS
| J. Propp, Updated article
J. Propp, Enumeration of matchings: problems and progress, in L. J. Billera et al. (eds.), New Perspectives in Algebraic Combinatorics
Index to sequences with linear recurrences with constant coefficients, signature (2,2,2,-1).
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FORMULA
| G.f.: (5 + 3*x + x^2 -x^3) / (1 - 2*x - 2*x^2 - 2*x^3 + x^4).
a(-n) = a(-5 + n). a(-1) = a(-2) = 1. a(n) = 2*a(n-1) + 2*a(n-2) + 2*a(n-3) - a(n-4). - Michael Somos, Dec 15 2011
A112835(2*n + 2) = a(n).
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EXAMPLE
| 5 + 13*x + 37*x^2 + 109*x^3 + 313*x^4 + 905*x^5 + 2617*x^6 + 7561*x^7 + ...
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PROG
| (PARI) {a(n) = local(m = n+2); if( m < 0, m = -1 - m); polcoeff( (1 - x + x^2 - x^3) / (1 - 2*x - 2*x^2 - 2*x^3 + x^4) + x * O(x^m), m)} /* Michael Somos, Dec 15 2011 */
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CROSSREFS
| Cf. A112835.
Sequence in context: A111057 A083413 A193642 * A199108 A125734 A146925
Adjacent sequences: A071097 A071098 A071099 * A071101 A071102 A071103
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), May 28 2002
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