OFFSET
1,2
LINKS
Eric Weisstein's World of Mathematics, Graph Cycle
Eric Weisstein's World of Mathematics, Grid Graph
FORMULA
a(n) = 2*A006772(n). - Andrey Zabolotskiy, Nov 09 2018
EXAMPLE
Let p(k,n) be the number of 2k-cycles in the n X n grid graph for n >= k-1. p(k,n) are quadratic polynomials in n, with the first few given by:
p(1,n) = 0,
p(2,n) = 1 - 2*n + n^2,
p(3,n) = 4 - 6*n + 2*n^2,
p(4,n) = 26 - 28*n + 7*n^2,
p(5,n) = 164 - 140*n + 28*n^2,
p(6,n) = 1046 - 740*n + 124*n^2,
p(7,n) = 6672 - 4056*n + 588*n^2,
p(8,n) = 42790 - 22904*n + 2938*n^2,
p(9,n) = 275888 - 132344*n + 15268*n^2,
...
The linear coefficients give a(n), so the first few are 0, 2, 6, 28, 140, .... - Eric W. Weisstein, Apr 05 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Apr 05 2018
EXTENSIONS
Terms a(12) and beyond added using data from A006772 by Andrey Zabolotskiy, Feb 10 2022
STATUS
approved