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A220864
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Number of perfect matchings in the graph C_4 X C_n.
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11
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50, 272, 722, 3108, 10082, 39952, 140450, 537636, 1956242, 7379216, 27246962, 102144036, 379501250, 1418981392, 5285770562, 19742287908, 73621286642, 274848860432, 1025412242450, 3827417932836, 14282150107682, 53304783436816, 198924689265122, 742414961433636, 2770663499604050, 10340361362903312
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OFFSET
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3,1
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LINKS
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FORMULA
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G.f.: 2*x^3*(25+36*x-333*x^2-6*x^3+467*x^4-104*x^5-71*x^6+18*x^7)/((1-x)*(1+x)*(1-4*x+x^2)*(1-2*x-x^2)*(1+2*x-x^2)). - Sergey Perepechko, Oct 21 2013
Assuming the above o.g.f. we have, for n >= 1, a(2n+1) = 2*A001834(n)^2 = (2 + sqrt(3))^(2*n+1) + (2 - sqrt(3))^(2*n+1) - 2. - Peter Bala, Apr 19 2014
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MATHEMATICA
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CoefficientList[Series[2 (25 + 36 x - 333 x^2 - 6 x^3 + 467 x^4 - 104 x^5 - 71 x^6 + 18 x^7)/((1 - x) (1 + x) (1 - 4 x + x^2) (1 - 2 x - x^2) (1 + 2 x - x^2)), {x, 0, 40}], x] (* Vincenzo Librandi, Apr 20 2014 *)
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PROG
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(PARI) Vec( 2*x^3*(25+36*x-333*x^2-6*x^3+467*x^4-104*x^5-71*x^6+18*x^7)/((1-x)*(1+x)*(1-4*x+x^2)*(1-2*x-x^2)*(1+2*x-x^2)) +O(x^66) ) \\ Joerg Arndt, Oct 22 2013
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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