A231485 Number of perfect matchings in the graph C_5 X C_{2n}.

722, 9922, 155682, 2540032, 41934482, 694861522, 11527389122, 191304901282, 3175220160032, 52703408458882, 874800747092322, 14520494659638322, 241020661471736882, 4000620276282860032, 66404949893677073282, 1102233473331064193122, 18295603728585969257522

Offset

2,1

Links

Colin Barker, Table of n, a(n) for n = 2..819

P. W. Kasteleyn, The Statistics of Dimers on a Lattice, Physica, 27 (1961), 1209-1225.

Index entries for linear recurrences with constant coefficients, signature (29,-261,1029,-2001,2001,-1029,261,-29,1).

Formula

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)).

From Seiichi Manyama, Feb 14 2021: (Start)

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)

Prog

(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

Crossrefs

Cf. A220864, A231087.

Sequence in context: A259721 A133531 A206006 * A035756 A107552 A232261

Adjacent sequences: A231482 A231483 A231484 * A231486 A231487 A231488

Keyword

nonn,easy

Author

Sergey Perepechko, Nov 09 2013

Status

approved