A266229 a(n) = Sum_{j=0..12} (-n)^j.
1, 1, 2731, 398581, 13421773, 203450521, 1865813431, 12111126301, 61083979321, 254186582833, 909090909091, 2876892678661, 8230246567621, 21633936185161, 52914318216943, 121637191772461, 264917625139441, 550254335161441
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
- OEIS Wiki, Cyclotomic Polynomials at x=n, n! and sigma(n)
- Eric Weisstein's World of Mathematics, Cyclotomic Polynomial
- Index to values of cyclotomic polynomials of integer argument
- Index entries for linear recurrences with constant coefficients, signature (13, -78, 286, -715, 1287, -1716, 1716, -1287, 715, -286, 78, -13, 1).
Crossrefs
Cf. similar sequences of the type Phi_k(n) listed in A269442.
Programs
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GAP
List([0..20], n-> Sum([0..12], j-> (-n)^j)); # G. C. Greubel, Apr 24 2019
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Magma
[(&+[(-n)^j: j in [0..12]]): n in [0..20]]; // G. C. Greubel, Apr 24 2019
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Mathematica
Table[n^12-n^11+n^10-n^9+n^8-n^7+n^6-n^5+n^4-n^3+n^2-n+1, {n, 0, 17}] Table[Cyclotomic[26, n], {n, 0, 17}] -
PARI
a(n) = polcyclo(26, n); \\ Michel Marcus, Mar 13 2016
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Sage
[sum((-n)^j for j in (0..12)) for n in (0..20)] # G. C. Greubel, Apr 24 2019
Formula
G.f.: (1 - 12*x + 2796*x^2 + 362870*x^3 + 8453667*x^4 + 59275152*x^5 + 155813880*x^6 + 167535876*x^7 + 74215935*x^8 + 12641708*x^9 + 691692*x^10 + 8022*x^11 + 13*x^12)/(1 - x)^13.
Sum_{n>=0} 1/a(n) = 2.0003687552...
Extensions
Name changed by G. C. Greubel, Apr 24 2019
Comments