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 A281583 Number of perfect matchings in the graph C_9 X C_{2n}. 7
 140450, 16091936, 2415542018, 400448833106, 69206906601800, 12190695635108354, 2167175327735637122, 387018647188487143424, 69272289588070930561250, 12413316310203106546620386, 2225719417041514241075539592, 399192630631160441128470998546 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS For odd values of m the order of recurrence relation for the number of perfect matchings in C_{m} X C_{2n} graph does not exceed 3^floor(m/2). LINKS Seiichi Manyama, Table of n, a(n) for n = 2..443 S. N. Perepechko, The number of perfect matchings on C_m X C_n graphs, (in Russian), Information Processes, 2016, V.16, No.4, pp.333-361. Sergey Perepechko, Generating function, in Maple notation. FORMULA a(n) = sqrt( Product_{j=1..n} Product_{k=1..9} (4*sin((2*j-1)*Pi/(2*n))^2 + 4*sin((2*k-1)*Pi/9)^2) ). - Seiichi Manyama, Feb 14 2021 PROG (PARI) default(realprecision, 120); a(n) = round(sqrt(prod(j=1, n, prod(k=1, 9, 4*sin((2*j-1)*Pi/(2*n))^2+4*sin((2*k-1)*Pi/9)^2)))); \\ Seiichi Manyama, Feb 14 2021 CROSSREFS Column k=9 of A341533. Cf. A253678, A230033, A232804, A231485, A220864, A231087. Sequence in context: A360843 A242143 A156409 * A186613 A036527 A250570 Adjacent sequences: A281580 A281581 A281582 * A281584 A281585 A281586 KEYWORD nonn AUTHOR Sergey Perepechko, Jan 25 2017 STATUS approved

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Last modified October 2 13:28 EDT 2023. Contains 365833 sequences. (Running on oeis4.)