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A339118 Number of cycles in the grid graph P_6 X P_n.

%I A339118 #15 Feb 16 2025 08:34:01
%S A339118 15,275,5034,80626,1222363,18438929,279285399,4237530095,64300829449,
%T A339118 975566486675,14800469958185,224540402345213,3406558215857382,
%U A339118 51681816786790684,784078741397570677,11895467318139343215,180469294422664219486,2737947622842077799930
%N A339118 Number of cycles in the grid graph P_6 X P_n.
%H A339118 Andrew Howroyd, <a href="/A339118/b339118.txt">Table of n, a(n) for n = 2..500</a>
%H A339118 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GraphCycle.html">Graph Cycle</a>
%H A339118 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GridGraph.html">Grid Graph</a>
%F A339118 Empirical g.f.: -x^2 * (15 - 325*x + 3889*x^2 - 32204*x^3 + 166496*x^4 - 439661*x^5 + 117553*x^6 + 2506529*x^7 - 5691052*x^8 - 128310*x^9 + 16209330*x^10 - 15148184*x^11 - 17089827*x^12 + 28709449*x^13 + 11141815*x^14 - 27136640*x^15 - 13792528*x^16 + 20876587*x^17 + 15963209*x^18 - 11646759*x^19 - 10681356*x^20 + 3192142*x^21 + 3419602*x^22 - 252986*x^23 - 401310*x^24 - 43774*x^25 + 13852*x^26 + 2950*x^27 - 278*x^28 - 48*x^29 + 4*x^30) / ((-1 + x)^2 * (-1 + 38*x - 580*x^2 + 4945*x^3 - 26274*x^4 + 84913*x^5 - 122213*x^6 - 183068*x^7 + 1124479*x^8 - 1544617*x^9 - 1129508*x^10 + 5346947*x^11 - 3023145*x^12 - 6147688*x^13 + 6904233*x^14 + 3952819*x^15 - 5690282*x^16 - 4144167*x^17 + 3164355*x^18 + 4915006*x^19 - 1267655*x^20 - 3336331*x^21 + 82962*x^22 + 1051157*x^23 + 93428*x^24 - 119962*x^25 - 23089*x^26 + 2688*x^27 + 1368*x^28 - 34*x^29 - 30*x^30 + 2*x^31)). - _Vaclav Kotesovec_, Dec 09 2020
%o A339118 (Python)
%o A339118 # Using graphillion
%o A339118 from graphillion import GraphSet
%o A339118 import graphillion.tutorial as tl
%o A339118 def A(n, k):
%o A339118     universe = tl.grid(n - 1, k - 1)
%o A339118     GraphSet.set_universe(universe)
%o A339118     cycles = GraphSet.cycles()
%o A339118     return cycles.len()
%o A339118 def A339118(n):
%o A339118     return A(6, n)
%o A339118 print([A339118(n) for n in range(2, 13)])
%Y A339118 Cf. A140517, A145401, A231829.
%K A339118 nonn
%O A339118 2,1
%A A339118 _Seiichi Manyama_, Nov 24 2020
%E A339118 Terms a(13) and beyond from _Andrew Howroyd_, Dec 08 2020