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 A050401 Number of independent sets of nodes in P_4 X C_n (n > 2). 2
 8, 1, 41, 142, 933, 4741, 26660, 143697, 788453, 4293286, 23454801, 127953981, 698467368, 3811712633, 20803963753, 113540081302, 619672701957, 3381980484909, 18457878595412, 100737602247769, 549796303339413 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (1,20,27,-14,-25,4,5,-1). FORMULA a(n) = a(n-1) + 20*a(n-2) + 27*a(n-3) - 14*a(n-4) - 25*a(n-5) + 4*a(n-6) + 5*a(n-7) - a(n-8). G.f.: -(5*x^7 +8*x^6 -75*x^5 -56*x^4 +135*x^3 +120*x^2 +7*x -8)/((x +1)*(x^2 -2*x -1)*(x^5 -4*x^4 -5*x^3 +9*x^2 +4*x -1)). [Colin Barker, Aug 31 2012] MATHEMATICA CoefficientList[Series[-(5 x^7 + 8 x^6 - 75 x^5 - 56 x^4 + 135 x^3 + 120 x^2 + 7 x - 8) / ((x + 1) (x^2 - 2 x - 1) (x^5 - 4 x^4 - 5 x^3 + 9 x^2 + 4 x - 1)), {x, 0, 50}], x] (* Vincenzo Librandi, May 11 2017 *) PROG (MAGMA) I:=[8, 1, 41, 142, 933, 4741, 26660, 143697]; [n le 8 select I[n] else Self(n-1)+20*Self(n-2)+27*Self(n-3)-14*Self(n-4)- 25*Self(n-5)+4*Self(n-6)+5*Self(n-7)-Self(n-8): n in [1..30]]; // Vincenzo Librandi, May 11 2017 CROSSREFS Column 4 of A286513. Sequence in context: A286919 A286260 A226374 * A271060 A318576 A089276 Adjacent sequences:  A050398 A050399 A050400 * A050402 A050403 A050404 KEYWORD easy,nonn AUTHOR Stephen G. Penrice (spenrice(AT)ets.org), Dec 21 1999 EXTENSIONS More terms from Michael Lugo (mlugo(AT)thelabelguy.com), Dec 22 1999 STATUS approved

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Last modified October 20 07:17 EDT 2018. Contains 316378 sequences. (Running on oeis4.)