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A304995
Expansion of (1 + 6*x + 6*x^2 + 6*x^3 + x^4 + 6*x^5)/((1 - x)*(1 + x^4)).
0
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].
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
KEYWORD
nonn,easy
AUTHOR
Shara Lalo, May 23 2018
STATUS
approved