A270204 a(n) = n^12 - n^10 + n^8 - n^6 + n^4 - n^2 + 1.
1, 1, 3277, 478297, 15790321, 234750601, 2117950381, 13564461457, 67662254017, 278985273841, 990099009901, 3112703553961, 8854610100337, 23161037562937, 56406126018061, 129172239050401, 280379743338241, 580613195032417, 1153271900252557, 2207200789455481
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..6], j-> (-n^2)^j)); # G. C. Greubel, Apr 24 2019
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Magma
[(&+[(-n^2)^j: j in [0..6]]): n in [0..20]]; // G. C. Greubel, Apr 24 2019
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Maple
a:= n-> add((-n^2)^j, j=0..6): seq(a(n), n=0..20); # Alois P. Heinz, Apr 24 2019
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Mathematica
Table[n^12 - n^10 + n^8 - n^6 + n^4 - n^2 + 1, {n, 0, 17}] Table[Cyclotomic[28, n], {n, 0, 17}] -
PARI
a(n) = polcyclo(28, n); \\ Altug Alkan, Mar 13 2016
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Sage
[sum((-n^2)^j for j in (0..6)) for n in (0..20)] # G. C. Greubel, Apr 24 2019
Formula
G.f.: (1 - 12*x + 3342*x^2 + 435488*x^3 + 9828495*x^4 + 65845800*x^5 + 163388148*x^6 + 163386432*x^7 + 65847087*x^8 + 9827780*x^9 + 435774*x^10 + 3264*x^11 + x^12)/(1 - x)^13.
Sum_{n>=0} 1/a(n) = 2.000307316...
Comments