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A003749
Number of Hamiltonian cycles in K_5 X P_n.
1
12, 480, 13440, 382080, 10859520, 308651520, 8772556800, 249335408640, 7086662123520, 201418564362240, 5724759747624960, 162710295705845760, 4624585396735180800, 131440914657055211520, 3735840635158368092160
OFFSET
1,1
REFERENCES
F. Faase, On the number of specific spanning subgraphs of the graphs G X P_n, Ars Combin. 49 (1998), 129-154.
LINKS
FORMULA
a(n) = 28a(n-1) + 12a(n-2), n>2.
G.f.: 12*x*(12*x^2-12*x-1)/(12*x^2+28*x-1). - Colin Barker, Aug 30 2012
MATHEMATICA
CoefficientList[Series[12 (12 x^2 - 12 x - 1)/(12 x^2 + 28 x - 1), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 14 2013 *)
PROG
(Magma) I:=[12, 480, 13440]; [n le 3 select I[n] else 28*Self(n-1)+12*Self(n-2): n in [1..20]]; // Vincenzo Librandi, Oct 14 2013
(PARI) a(n)=([0, 1; 12, 28]^(n-1)*[12; 480])[1, 1] \\ Charles R Greathouse IV, Jun 23 2020
CROSSREFS
Sequence in context: A262584 A350154 A241226 * A012395 A012687 A012467
KEYWORD
nonn,easy
STATUS
approved