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A001559
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a(0) = 1, a(1) = 4; thereafter a(n) * (2*n + 10) - a(n-1) * (11*n + 35) + a(n-2) * (8*n + 2) + a(n-3) * (15*n + 7) + a(n-4) * (4*n - 2) = 0.
(Formerly M3497 N1418)
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2
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1, 4, 15, 54, 193, 690, 2476, 8928, 32358, 117866, 431381, 1585842, 5853849, 21690378, 80650536, 300845232, 1125555054, 4222603968, 15881652606, 59873283372, 226214536506, 856431978324, 3248562071800, 12344168149224
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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REFERENCES
| Fine, Terrence; Extrapolation when very little is known about the source. Information and Control 16 (1970), 331-359.
S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/MasterThesis.pdf">Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures</a>, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, < a href="http://arxiv.org/ftp/arxiv/papers/0912/0912.0072.pdf"> Une méthode pour obtenir la fonction génératrice d'une série. FPSAC 1993, Florence. Formal Power Series and Algebraic Combinatorics.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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FORMULA
| 0 = -a(n) * n * (2*n + 10) * (7*n + 13) + a(n-1) * (49*n^3 + 252*n^2 + 419*n + 240) + a(n-2) * (2*n + 2) * (2*n + 3) * (7*n + 20). - Michael Somos Jul 14 2009
G.f.: 2 / (1 - 4*x + x^2 + 2*x^3 + (1 - 2*x - x^2) * sqrt(1 - 4*x )). - Michael Somos Jul 14 2009
(n + 4) a(n) = (- 15/2 n + 4) a(n - 3) + (11/2 n + 12) a(n - 1)
+ (- 4 n + 3) a(n - 2) + (- 2 n + 3) a(n - 4). [Simon Plouffe, Feb 09 2012]
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EXAMPLE
| 1 + 4*x + 15*x^2 + 54*x^3 + 193*x^4 + 690*x^5 + 2476*x^6 + 8928*x^7 + ...
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PROG
| (PARI) {a(n) = if( n<0, 0, polcoeff( 2 / (1 - 4*x + x^2 + 2*x^3 + (1 - 2*x - x^2) * sqrt(1 - 4*x + x*O(x^n))), n))}; /* Michael Somos Jul 14 2009 */
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CROSSREFS
| Sequence in context: A006234 A094821 A071723 * A002311 A102349 A126932
Adjacent sequences: A001556 A001557 A001558 * A001560 A001561 A001562
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KEYWORD
| nonn,changed
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Better definition and more terms from Michael Somos, Jul 14 2009
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