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A302335 Constant coefficient of the quadratic polynomials giving the numbers of 2k-cycles in the n X n grid graph for n >= k-1.

%I A302335 #23 Feb 10 2022 07:22:36
%S A302335 0,1,4,26,164,1046,6672,42790,275888,1787624,11634704
%N A302335 Constant coefficient of the quadratic polynomials giving the numbers of 2k-cycles in the n X n grid graph for n >= k-1.
%C A302335 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 A302335 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GraphCycle.html">Graph Cycle</a>
%H A302335 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GridGraph.html">Grid Graph</a>
%e A302335 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 A302335 p(1,n) = 0,
%e A302335 p(2,n) = 1 - 2*n + n^2,
%e A302335 p(3,n) = 4 - 6*n + 2*n^2,
%e A302335 p(4,n) = 26 - 28*n + 7*n^2,
%e A302335 p(5,n) = 164 - 140*n + 28*n^2,
%e A302335 p(6,n) = 1046 - 740*n + 124*n^2,
%e A302335 p(7,n) = 6672 - 4056*n + 588*n^2,
%e A302335 p(8,n) = 42790 - 22904*n + 2938*n^2,
%e A302335 p(9,n) = 275888 - 132344*n + 15268*n^2,
%e A302335 ...
%e A302335 The constant coefficients give a(n), so the first few are 0, 1, 4, 26, 164, .... - _Eric W. Weisstein_, Apr 05 2018
%Y A302335 Cf. A302336 (linear coefficients).
%Y A302335 Cf. A002931 (quadratic coefficients).
%K A302335 nonn,more
%O A302335 1,3
%A A302335 _Eric W. Weisstein_, Apr 05 2018