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

Author

Sergey Perepechko, Jan 26 2017

Keywords

• nonn

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.