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 A195197 Number of Hamiltonian cycles in the generalized Petersen Graph P(n,2). 1
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 3,1 LINKS 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). FORMULA 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 ) MAPLE 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: MATHEMATICA 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 *) CROSSREFS Sequence in context: A196609 A070063 A016668 * A154462 A112255 A197417 Adjacent sequences:  A195194 A195195 A195196 * A195198 A195199 A195200 KEYWORD nonn,easy AUTHOR R. J. Mathar, Sep 11 2011 STATUS approved

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Last modified June 26 10:23 EDT 2022. Contains 354879 sequences. (Running on oeis4.)