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A195197
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Number of Hamiltonian cycles in the generalized Petersen Graph P(n,2).
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1
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3, 8, 0, 6, 7, 12, 3, 30, 0, 34, 13, 56, 3, 108, 0, 150, 19, 244, 3, 418, 0, 642, 25, 1040, 3, 1712, 0, 2726, 31, 4412, 3, 7174, 0, 11554, 37, 18696, 3, 30292, 0, 48950, 43, 79204, 3, 128202, 0, 207362, 49, 335520
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OFFSET
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3,1
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 3..1000
A. J. Schwenk, Enumeration of Hamiltonian cycles in certain generalized Petersen graphs, J. Combin. Theory B 47 (1) (1989) 53-59.
Index entries for linear recurrences with constant coefficients, signature (0, 1, 1, 1, -1, 1, -1, -1, -1, -1, 1, 0, 1).
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FORMULA
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G.f. -x^3*(3 +8*x -5*x^3 -4*x^4 +x^5 -5*x^6 +x^9 +2*x^10 +x^11 -3*x^2 -5*x^8) / ( (1+x) *(x^2-x+1) *(x^4+x^2-1) *(x-1)^2 *(1+x+x^2)^2 )
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MAPLE
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A195197 := proc(n)
if modp(n, 6) =0 or modp(n, 6) = 2 then
2*(combinat[fibonacci](n/2+2)-combinat[fibonacci](n/2-2)-1) ;
elif modp(n, 6) = 1 then
n;
elif modp(n, 6) = 3 then
3;
elif modp(n, 6) = 4 then
n+2*(combinat[fibonacci](n/2+2)-combinat[fibonacci](n/2-2)-1) ;
else
0;
end if;
end proc:
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MATHEMATICA
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CoefficientList[Series[-(3 + 8*x - 5*x^3 - 4*x^4 + x^5 - 5*x^6 + x^9 + 2*x^10 + x^11 - 3*x^2 - 5*x^8)/((1+x)*(x^2-x+1)*(x^4+x^2-1)*(x-1)^2*(1+x+x^2)^2), {x, 0, 60}], x] (* Vincenzo Librandi, Dec 23 2012 *)
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CROSSREFS
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Sequence in context: A196609 A070063 A016668 * A154462 A112255 A197417
Adjacent sequences: A195194 A195195 A195196 * A195198 A195199 A195200
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KEYWORD
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nonn,easy
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AUTHOR
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R. J. Mathar, Sep 11 2011
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STATUS
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approved
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