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A060884 a(n) = n^4 - n^3 + n^2 - n + 1. 14
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

LINKS

Harry J. Smith, Table of n, a(n) for n = 0..1000

Index to values of cyclotomic polynomials of integer argument

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

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

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 December 6 06:58 EST 2016. Contains 278775 sequences.