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

0,3

Comments

a(n) = Phi_28(n) where Phi_k(x) is the k-th cyclotomic polynomial.

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).

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...

Maple

a:= n-> add((-n^2)^j, j=0..6):
seq(a(n), n=0..20);  # Alois P. Heinz, Apr 24 2019

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}]

Prog

(PARI) a(n) = polcyclo(28, n); \\ Altug Alkan, Mar 13 2016
(Magma) [(&+[(-n^2)^j: j in [0..6]]): n in [0..20]]; // G. C. Greubel, Apr 24 2019
(SageMath) [sum((-n^2)^j for j in (0..6)) for n in (0..20)] # G. C. Greubel, Apr 24 2019
(GAP) List([0..20], n-> Sum([0..6], j-> (-n^2)^j)); # G. C. Greubel, Apr 24 2019

Crossrefs

Cf. similar sequences of the type Phi_k(n) listed in A269442.

Sequence in context: A245482 A356638 A244626 * A293626 A152506 A309284

Adjacent sequences: A270201 A270202 A270203 * A270205 A270206 A270207

Keyword

nonn,easy

Author

Ilya Gutkovskiy, Mar 13 2016

Status

approved