A060888 - OEIS

%I #36 Apr 23 2023 07:26:40

%S 1,1,43,547,3277,13021,39991,102943,233017,478297,909091,1623931,

%T 2756293,4482037,7027567,10678711,15790321,22796593,32222107,44693587,

%U 60952381,81867661,108450343,141867727,183458857,234750601,297474451,373584043,465273397,574995877

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

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

%C 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

%C 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

%H Harry J. Smith, <a href="/A060888/b060888.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Cy#CyclotomicPolynomialsValuesAtX">Index to values of cyclotomic polynomials of integer argument</a>

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).

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

%F 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

%F 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

%p A060888 := proc(n)

%p         numtheory[cyclotomic](14,n) ;

%p end proc:

%p seq(A060888(n),n=0..20) ; # _R. J. Mathar_, Feb 11 2014

%t 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 *)

%o (PARI) { for (n=0, 1000, write("b060888.txt", n, " ", n^6 - n^5 + n^4 - n^3 + n^2 - n + 1); ) } \\ _Harry J. Smith_, Jul 14 2009

%K nonn,easy

%O 0,3

%A _N. J. A. Sloane_, May 05 2001