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A003744 Number of Hamiltonian paths in O_5 X P_n.

%I A003744 #17 Jan 01 2019 06:31:05
%S A003744 36,3960,197172,8372376,313590732,10961493288,364496212992,
%T A003744 11715923002644,367218115613412,11297962590845364,342721436917704060,
%U A003744 10284809936813182116,306078425919342660924
%N A003744 Number of Hamiltonian paths in O_5 X P_n.
%D A003744 F. Faase, On the number of specific spanning subgraphs of the graphs G X P_n, Ars Combin. 49 (1998), 129-154.
%H A003744 Sean A. Irvine, <a href="/A003744/b003744.txt">Table of n, a(n) for n = 1..100</a>
%H A003744 F. Faase, <a href="http://www.iwriteiam.nl/Cpaper.zip">On the number of specific spanning subgraphs of the graphs G X P_n</a>, Preliminary version of paper that appeared in Ars Combin. 49 (1998), 129-154.
%H A003744 F. Faase, <a href="http://www.iwriteiam.nl/counting.html">Counting Hamiltonian cycles in product graphs</a>
%H A003744 F. Faase, <a href="http://www.iwriteiam.nl/Cresults.html">Results from the counting program</a>
%F A003744 a(1) = 36,
%F A003744 a(2) = 3960,
%F A003744 a(3) = 197172,
%F A003744 a(4) = 8372376,
%F A003744 a(5) = 313590732,
%F A003744 a(6) = 10961493288,
%F A003744 a(7) = 364496212992,
%F A003744 a(8) = 11715923002644,
%F A003744 a(9) = 367218115613412,
%F A003744 a(10) = 11297962590845364,
%F A003744 a(11) = 342721436917704060,
%F A003744 a(12) = 10284809936813182116,
%F A003744 a(13) = 306078425919342660924,
%F A003744 a(14) = 9050314137435866812308,
%F A003744 a(15) = 266262758895847900204044,
%F A003744 a(16) = 7802857128214786920966468,
%F A003744 a(17) = 227964188131745757879553596,
%F A003744 a(18) = 6644168196971243295712163700,
%F A003744 a(19) = 193287318120848681996183075244,
%F A003744 a(20) = 5614785173559337471057013732388,
%F A003744 a(21) = 162918194408431653609336890189340,
%F A003744 a(22) = 4723043996602440520832973512325972,
%F A003744 a(23) = 136828273928341927052870400623002380, and
%F A003744 a(n) = 59a(n-1) - 731a(n-2) - 11403a(n-3) + 204688a(n-4) + 697232a(n-5)
%F A003744 - 13575824a(n-6) + 15466532a(n-7) + 288258520a(n-8) - 1327022000a(n-9) + 1631290560a(n-10)
%F A003744 + 3212771840a(n-11) - 12023726208a(n-12) + 9649896000a(n-13) + 11298643072a(n-14) - 24109594624a(n-15)
%F A003744 + 6239014400a(n-16) + 14028280832a(n-17) - 8564428800a(n-18) - 2763866112a(n-19) + 2175729664a(n-20)
%F A003744 + 199229440a(n-21) - 150994944a(n-22).
%K A003744 nonn
%O A003744 1,1
%A A003744 _Frans J. Faase_
%E A003744 Added recurrence from Faase's web page. - _N. J. A. Sloane_, Feb 03 2009