%I #23 Feb 10 2022 07:22:36
%S 0,1,4,26,164,1046,6672,42790,275888,1787624,11634704
%N Constant coefficient of the quadratic polynomials giving the numbers of 2k-cycles in the n X n grid graph for n >= k-1.
%C a(n) is the sum of the areas of minimal bounding rectangles of (fixed, self-avoiding) 2n-cycles in a grid. - _Andrey Zabolotskiy_, Feb 09 2022
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GraphCycle.html">Graph Cycle</a>
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GridGraph.html">Grid Graph</a>
%e 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:
%e p(1,n) = 0,
%e p(2,n) = 1 - 2*n + n^2,
%e p(3,n) = 4 - 6*n + 2*n^2,
%e p(4,n) = 26 - 28*n + 7*n^2,
%e p(5,n) = 164 - 140*n + 28*n^2,
%e p(6,n) = 1046 - 740*n + 124*n^2,
%e p(7,n) = 6672 - 4056*n + 588*n^2,
%e p(8,n) = 42790 - 22904*n + 2938*n^2,
%e p(9,n) = 275888 - 132344*n + 15268*n^2,
%e ...
%e The constant coefficients give a(n), so the first few are 0, 1, 4, 26, 164, .... - _Eric W. Weisstein_, Apr 05 2018
%Y Cf. A302336 (linear coefficients).
%Y Cf. A002931 (quadratic coefficients).
%K nonn,more
%O 1,3
%A _Eric W. Weisstein_, Apr 05 2018