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A180585 Number of Hamiltonian cycles in C_9 X P_n.

%I A180585 #13 Feb 18 2025 16:30:15
%S A180585 1,9,510,12348,351258,9806292,276018090,7769376972,218915964618,
%T A180585 6169925169414,173923080282474,4903042542453720,138226113213225360,
%U A180585 3896923927019062734,109864493967924549384,3097380080814655131414,87323767337933601800838,2461902328199084994926838
%N A180585 Number of Hamiltonian cycles in C_9 X P_n.
%H A180585 Andrew Howroyd, <a href="/A180585/b180585.txt">Table of n, a(n) for n = 1..200</a>
%H A180585 Artem M. Karavaev, FlowProblem.ru web-project: <a href="https://web.archive.org/web/20161024010518/http://flowproblem.ru/cycles/hamilton-cycles">Hamilton Cycles</a> page.
%H A180585 <a href="/index/Rec#order_51">Index entries for linear recurrences with constant coefficients</a>, order 51.
%F A180585 a(n) = -188416a(n-51) + 835584a(n-50) + 7955456a(n-49) - 41793024a(n-48) -
%F A180585 33238528a(n-47) + 334600192a(n-46) - 1276157184a(n-45) + 2732681344a(n-44) -
%F A180585 2618432768a(n-43) - 5036989056a(n-42) + 11060535424a(n-41) + 27959018048a(n-40) -
%F A180585 52440361440a(n-39) - 37908518240a(n-38) + 74330191136a(n-37) + 59186108112a(n-36) -
%F A180585 68887152928a(n-35) - 33605932304a(n-34) + 43670159120a(n-33) + 48309187400a(n-32) +
%F A180585 33949381128a(n-31) + 12462888472a(n-30) - 88313767808a(n-29) - 107865096688a(n-28) +
%F A180585 20762733116a(n-27) + 153311805598a(n-26) + 152573320432a(n-25) + 38397703554a(n-24) -
%F A180585 70575876534a(n-23) - 117036064104a(n-22) - 90546530362a(n-21) - 20062310737a(n-20) +
%F A180585 30892900555a(n-19) + 30318783786a(n-18) + 6586175756a(n-17) - 5975151103a(n-16) -
%F A180585 4972136691a(n-15) - 2026783228a(n-14) - 1418765189a(n-13) - 1239197497a(n-12) -
%F A180585 576571223a(n-11) - 60031321a(n-10) + 63704924a(n-9) + 32475252a(n-8) + 6586040a(n-7) +
%F A180585 334567a(n-6) - 152710a(n-5) - 38447a(n-4) - 2238a(n-3) + 280a(n-2) + 23a(n-1), n>52.
%Y A180585 Column k=9 of A359855.
%K A180585 nonn,easy
%O A180585 1,2
%A A180585 _Artem M. Karavaev_, Sep 10 2010
%E A180585 a(17) onwards from _Andrew Howroyd_, Feb 18 2025