

A060884


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


12



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
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OFFSET

0,3


COMMENTS

a(n) = Phi_10(n), where Phi_k is the kth 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^4t^3+t^2t+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.: (14*x+16*x^2+6*x^3+5*x^4)/(1x)^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



