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A145407 Number of Hamiltonian paths in O_6 X P_n. 1

%I

%S 120,41280,6641952,886927344,105209243232,16691618745408,

%T 3453770804410752,830385563124340992,212352384742765204992,

%U 55504372130542230537216,14614230909478166949599232

%N Number of Hamiltonian paths in O_6 X P_n.

%D F. Faase, On the number of specific spanning subgraphs of the graphs G X P_n, Ars Combin. 49 (1998), 129-154.

%H 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 F. Faase, <a href="http://www.iwriteiam.nl/counting.html">Counting Hamiltonian cycles in product graphs</a>.

%H F. Faase, <a href="http://www.iwriteiam.nl/Cresults.html">Results from the counting program</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (350,-22608,-17280,843264).

%F Recurrence:

%F a(1) = 120,

%F a(2) = 41280,

%F a(3) = 6641952,

%F a(4) = 886927344,

%F a(5) = 105209243232, and

%F a(n) = 350a(n-1) - 22608a(n-2) - 17280a(n-3) + 843264a(n-4).

%F G.f.: 24*x*(2268414568*x^4 +20934334*x^3 +212212*x^2 +30*x -5)/((6*x -1)*(140544*x^3 +20544*x^2 -344*x +1)). [_Colin Barker_, Aug 31 2012]

%p A145407 := proc(n) option remember; if n <= 5 then op(n,[120, 41280, 6641952, 886927344, 105209243232]) ; else 350*procname(n-1)- 22608*procname(n-2) - 17280*procname(n-3) + 843264*procname(n-4); fi; end: seq(A145407(n),n=1..20) ; # _R. J. Mathar_, Mar 14 2009

%t Join[{120}, LinearRecurrence[{350, -22608, -17280, 843264}, {41280, 6641952, 886927344, 105209243232}, 10]] (* _Jean-Fran├žois Alcover_, Apr 04 2020 *)

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_, Feb 03 2009

%E More terms from _R. J. Mathar_, Mar 14 2009

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Last modified November 23 21:51 EST 2020. Contains 338603 sequences. (Running on oeis4.)