A304995 Expansion of (1 + 6*x + 6*x^2 + 6*x^3 + x^4 + 6*x^5)/((1 - x)*(1 + x^4)).

1, 7, 13, 19, 19, 19, 13, 7, 7, 7, 13, 19, 19, 19, 13, 7, 7, 7, 13, 19, 19, 19, 13, 7, 7, 7, 13, 19, 19, 19, 13, 7, 7, 7, 13, 19, 19, 19, 13, 7, 7, 7, 13, 19, 19, 19, 13, 7, 7, 7, 13, 19, 19, 19, 13, 7, 7, 7, 13, 19, 19, 19, 13, 7, 7, 7, 13, 19, 19, 19, 13, 7, 7, 7, 13, 19, 19, 19

Offset

0,2

Comments

After the first term, the sequence is periodic with period 8: repeat [7, 13, 19, 19, 19, 13, 7, 7].

Links

Table of n, a(n) for n=0..77.

Index entries for linear recurrences with constant coefficients, signature (1,0,0,-1,1).

Formula

G.f.: (1 + 6*x + 6*x^2 + 6*x^3 + x^4 + 6*x^5)/((1 - x)*(1 + x^4)).

a(n) = 13 - 3*cos((Pi/8)*(1 + 2*n - 2*cos(n*Pi/2) + cos(n*Pi) - 2*sin(n*Pi/2))) - 3*cos((Pi/8)*(1 - 2*n - 2*cos(n*Pi/2) + cos(n*Pi) + 2*sin(n*Pi/2))) for n > 0 with a(0)=1. - Wesley Ivan Hurt, Oct 06 2018

Mathematica

CoefficientList[ Series[(1 + 6 x + 6 x^2 + 6 x^3 + x^4 + 6 x^5)/((1 - x) (1 + x^4)), {x, 0, 103}], x]

Crossrefs

Sequence in context: A254762 A275681 A173928 * A339657 A330946 A160007

Adjacent sequences: A304992 A304993 A304994 * A304996 A304997 A304998

Keyword

nonn,easy

Author

Shara Lalo, May 23 2018

Status

approved