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A001582
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Product of Fibonacci and Pell numbers.
(Formerly M1966 N0779)
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2
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1, 2, 10, 36, 145, 560, 2197, 8568, 33490, 130790, 510949, 1995840, 7796413, 30454814, 118965250, 464711184, 1815292333, 7091038640, 27699580729, 108202305420, 422668460890, 1651061182538, 6449506621417, 25193576136960
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Also number of perfect matchings (or domino tilings) in the graph W_4 X P_n.
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REFERENCES
| J. L. Diaz-Barrero and J. J. Egozcue, Problem H-605, Fib. Q., 43 (No. 1, 2005), 92.
D. C. Mead, An elementary method of summation, Fib. Quart. 3 (1965), 209-213.
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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LINKS
| T. D. Noe, Table of n, a(n) for n=0..200
F. Faase, Counting Hamilton cycles in product graphs
F. Faase, Counting Hamilton cycles in product graphs
F. Faase, Results from the counting program
S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
James A. Sellers, Domino Tilings and Products of Fibonacci and Pell Numbers, Journal of Integer Sequences, Vol. 5 (2002), Article 02.1.2
Index entries for sequences related to dominoes
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FORMULA
| G.f.: (1-x^2)/(1-2*x-7*x^2-2*x^3+x^4).
a(n)=11a(n-2)+16a(n-3)+3a(n-4)-2a(n-5). a(n)=2a(n-1)+7a(n-2)+2a(n-3)-a(n-4). [From Kieren MacMillan (kieren(AT)alumni.rice.edu), Sep 29 2008]
a(n)=((10+5*sqrt(2)+2*sqrt(5)+sqrt(10))*((1+sqrt(2)+sqrt(5)+sqrt(10))/2)^n+(10-5*sqrt(2)-2*sqrt(5)+sqrt(10))*((1-sqrt(2)-sqrt(5)+sqrt(10))/2)^n+(10+5*sqrt(2)-2*sqrt(5)-sqrt(10))*((1+sqrt(2)-sqrt(5)-sqrt(10))/2)^n+(10-5*sqrt(2)+2*sqrt(5)-sqrt(10))*((1-sqrt(2)+sqrt(5)-sqrt(10))/2)^n)/40. [Tim Monahan Aug 3 2011]
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MAPLE
| A001582:=-(z-1)*(1+z)/(1-2*z-7*z**2-2*z**3+z**4); [Conjectured (correctly) by S. Plouffe in his 1992 dissertation.]
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MATHEMATICA
| CoefficientList[Series[(1-x^2)/(1-2x-7x^2-2x^3+x^4), {x, 0, 30}], x] (* or *) LinearRecurrence[{2, 7, 2, -1}, {1, 2, 10, 36}, 30] (* From Harvey P. Dale, May 01 2011 *)
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CROSSREFS
| Cf. A000045, A000129.
Sequence in context: A206622 A192858 A202796 * A026546 A151020 A151021
Adjacent sequences: A001579 A001580 A001581 * A001583 A001584 A001585
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from James A. Sellers (sellersj(AT)math.psu.edu), May 01 2000
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