A281679 Number of perfect matchings in the graph C_10 X C_n.

5054, 537636, 2540032, 114557000, 1034315998, 33898728836, 400448833106, 11203604497408, 152849502772958, 3876306765700644, 58099728840105682, 1375359477482867528, 22057225099289357824, 496348449090698237956, 8370856315868909044082, 181385918483215101487880

Offset

3,1

Comments

For even values of m the order of recurrence relation for the number of perfect matchings in C_m X C_n graph does not exceed (3^delta(m/2) + 2*(3/5)^(1 - delta(m/2)))*5^floor(m/4) + 1. Here delta(k) equals 1 for odd values of k and 0 otherwise. If m=10 the above estimate gives 126 for the order of recurrence relation while the exact value equals 118.

Links

Seiichi Manyama, Table of n, a(n) for n = 3..500

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.

Eric Weisstein's World of Mathematics, Independent Edge Set

Eric Weisstein's World of Mathematics, Matching

Eric Weisstein's World of Mathematics, Perfect Matching

Eric Weisstein's World of Mathematics, Torus Grid Graph

Crossrefs

Row n=5 of A341741.

Cf. A220864, A230033, A231087, A231485, A232804, A253678, A281583.

Sequence in context: A031749 A229857 A155145 * A187356 A187354 A160757

Adjacent sequences: A281676 A281677 A281678 * A281680 A281681 A281682

Keyword

nonn

Author

Sergey Perepechko, Jan 26 2017

Status

approved