A060888 a(n) = n^6 - n^5 + n^4 - n^3 + n^2 - n + 1.

1, 1, 43, 547, 3277, 13021, 39991, 102943, 233017, 478297, 909091, 1623931, 2756293, 4482037, 7027567, 10678711, 15790321, 22796593, 32222107, 44693587, 60952381, 81867661, 108450343, 141867727, 183458857, 234750601, 297474451, 373584043, 465273397, 574995877

Offset: 0

Author

N. J. A. Sloane, May 05 2001

Keywords

• nonn
• easy

Comments

a(n) = Phi_14(n) where Phi_k is the k-th cyclotomic polynomial.

Number of walks of length 7 between any two distinct nodes of the complete graph K_{n+1} (n>=1). - Emeric Deutsch, Apr 01 2004

For odd n, a(n) * (n+1) / 2 also represents the first integer in a sum of n^7 consecutive integers that equals n^14. - Patrick J. McNab, Dec 26 2016

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 (7,-21,35,-35,21,-7,1).

Programs

Maple

A060888 := proc(n)
        numtheory[cyclotomic](14,n) ;
end proc:
seq(A060888(n),n=0..20) ; # R. J. Mathar, Feb 11 2014

Mathematica

Table[1-n+n^2-n^3+n^4-n^5+n^6,{n,0,30}] (* or *) LinearRecurrence[ {7,-21,35,-35,21,-7,1},{1,1,43,547,3277,13021,39991},30] (* or *) Cyclotomic[14,Range[0,30]] (* Harvey P. Dale, Jul 21 2012 *)

PARI

a(n) = { n^6 - n^5 + n^4 - n^3 + n^2 - n + 1 } \\ Harry J. Smith, Jul 14 2009

Formula

G.f.: (1 - 6x + 57x^2 + 232x^3 + 351x^4 + 78x^5 + 7x^6)/(1-x)^7. - Emeric Deutsch, Apr 01 2004

a(0)=1, a(1)=1, a(2)=43, a(3)=547, a(4)=3277, a(5)=13021, a(6)=39991, a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7). - Harvey P. Dale, Jul 21 2012

E.g.f.: exp(x)*(1 + 21*x^2 +70*x^3 + 56*x^4 + 14*x^5 + x^6). - Stefano Spezia, Apr 22 2023