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 A060884 a(n) = n^4 - n^3 + n^2 - n + 1. 16
 1, 1, 11, 61, 205, 521, 1111, 2101, 3641, 5905, 9091, 13421, 19141, 26521, 35855, 47461, 61681, 78881, 99451, 123805, 152381, 185641, 224071, 268181, 318505, 375601, 440051, 512461, 593461, 683705, 783871, 894661, 1016801, 1151041 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS a(n) = Phi_10(n), where Phi_k is the k-th cyclotomic polynomial. Number of walks of length 5 between any two distinct nodes of the complete graph K_{n+1} (n>=1). Example: a(1)=1 because in the complete graph AB we have only one walk of length 5 between A and B: ABABAB. - Emeric Deutsch, Apr 01 2004 t^4-t^3+t^2-t+1 is the Alexander polynomial (with negative powers cleared) of the cinquefoil knot (torus knot T(5,2)). The associated Seifert matrix S is [[ -1, -1, 0, -1], [ 0, -1, 0, 0], [ -1, -1, -1, -1], [ 0, -1, 0, -1]]. a(n) = det(transpose(S)-n*S). Cf. A084849. - Peter Bala, Mar 14 2012 For odd n, a(n) * (n+1) / 2 also represents the first integer in a sum of n^5 consecutive integers that equals n^10. - Patrick J. McNab, Dec 26 2016 LINKS Ray Chandler, Table of n, a(n) for n = 0..10000 (first 1001 terms from Harry J. Smith) Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1). FORMULA G.f.: (1-4*x+16*x^2+6*x^3+5*x^4)/(1-x)^5. - Emeric Deutsch, Apr 01 2004 MAPLE A060884 := proc(n)         numtheory[cyclotomic](10, n) ; end proc: seq(A060884(n), n=0..20) ; # R. J. Mathar, Feb 07 2014 MATHEMATICA Table[1 + Fold[(-1)^(#2)*n^(#2) + #1 &, Range[0, 4]], {n, 0, 33}] (* or *) CoefficientList[Series[(1 - 4 x + 16 x^2 + 6 x^3 + 5 x^4)/(1 - x)^5, {x, 0, 33}], x] (* Michael De Vlieger, Dec 26 2016 *) Table[n^4-n^3+n^2-n+1, {n, 0, 40}] (* or *) LinearRecurrence[{5, -10, 10, -5, 1}, {1, 1, 11, 61, 205}, 40] (* Harvey P. Dale, Sep 08 2018 *) PROG (PARI) { for (n=0, 1000, write("b060884.txt", n, " ", n^4 - n^3 + n^2 - n + 1); ) } \\ Harry J. Smith, Jul 13 2009 CROSSREFS Cf. A084849, A246392, A259257. Sequence in context: A078554 A189227 A002650 * A141935 A222408 A001847 Adjacent sequences:  A060881 A060882 A060883 * A060885 A060886 A060887 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, May 05 2001 STATUS approved

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Last modified October 6 12:35 EDT 2022. Contains 357264 sequences. (Running on oeis4.)