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A231485
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Number of perfect matchings in the graph C_5 X C_{2n}.
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11
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722, 9922, 155682, 2540032, 41934482, 694861522, 11527389122, 191304901282, 3175220160032, 52703408458882, 874800747092322, 14520494659638322, 241020661471736882, 4000620276282860032, 66404949893677073282, 1102233473331064193122, 18295603728585969257522
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OFFSET
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2,1
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LINKS
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FORMULA
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G.f.: 2*x^2*(361-5508*x+28193*x^2-64021*x^3+70770*x^4-38841*x^5+10278*x^6-1173*x^7+41*x^8)/((1-x)*(1-9*x+21*x^2-9*x^3+x^4)*(1-19*x+41*x^2-19*x^3+x^4)).
a(n) = sqrt( Product_{j=1..n} Product_{k=1..5} (4*sin((2*j-1)*Pi/(2*n))^2 + 4*sin((2*k-1)*Pi/5)^2) ).
a(n) = 28*a(n-1) - 233*a(n-2) + 796*a(n-3) - 1205*a(n-4) + 796*a(n-5) - 233*a(n-6) + 28*a(n-7) - a(n-8) + 200. (End)
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PROG
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(PARI) Vec(2*x^2*(361-5508*x+28193*x^2-64021*x^3+70770*x^4-38841*x^5+10278*x^6-1173*x^7+41*x^8)/((1-x)*(1-9*x+21*x^2-9*x^3+x^4)*(1-19*x+41*x^2-19*x^3+x^4)) + O(x^100)) \\ Colin Barker, Dec 13 2014
(PARI) default(realprecision, 120);
a(n) = round(sqrt(prod(j=1, n, prod(k=1, 5, 4*sin((2*j-1)*Pi/(2*n))^2+4*sin((2*k-1)*Pi/5)^2)))); \\ Seiichi Manyama, Feb 14 2021
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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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STATUS
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approved
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