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%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
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