A117451 Expansion of (1-x+x^2+x^5)/((1-x)*(1-x^5)).

1, 0, 1, 1, 1, 3, 2, 3, 3, 3, 5, 4, 5, 5, 5, 7, 6, 7, 7, 7, 9, 8, 9, 9, 9, 11, 10, 11, 11, 11, 13, 12, 13, 13, 13, 15, 14, 15, 15, 15, 17, 16, 17, 17, 17, 19, 18, 19, 19, 19, 21, 20, 21, 21, 21, 23, 22, 23, 23, 23, 25, 24, 25, 25, 25, 27, 26, 27, 27, 27, 29, 28, 29, 29, 29, 31, 30, 31

Offset

0,6

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

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

Formula

a(n) = a(n-1) + a(n-5) - a(n-6).

a(n) = -1 + ((5 + sqrt(5))/10)*cos(4*Pi*n/5) - sqrt(((5 - sqrt(5))/250)*sin(4*Pi*n/5) + ((5-sqrt(5))/10)*cos(2*Pi*n/5) + sqrt((5+sqrt(5))/250)*sin(2*Pi*n/5) + (2*n + 5)/5.

a(n) = A117450(n) - A117450(n-1). - G. C. Greubel, Jun 03 2021

Mathematica

CoefficientList[Series[(1-x+x^2+x^5)/((1-x)(1-x^5)), {x, 0, 80}], x] (* or *) LinearRecurrence[{1, 0, 0, 0, 1, -1}, {1, 0, 1, 1, 1, 3}, 80] (* Harvey P. Dale, Jan 01 2016 *)

Prog

(Magma) R<x>:=PowerSeriesRing(Integers(), 80); Coefficients(R!( (1-x+x^2+x^5)/((1-x)*(1-x^5)) )); // G. C. Greubel, Jun 03 2021
(Sage)
def A117451_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( (1-x+x^2+x^5)/((1-x)*(1-x^5)) ).list()
A117451_list(80) # G. C. Greubel, Jun 03 2021

Crossrefs

Partial sums are A117450. Partial sums of A117452.

Sequence in context: A086920 A182021 A370231 * A130970 A144733 A091460

Adjacent sequences: A117448 A117449 A117450 * A117452 A117453 A117454

Keyword

easy,nonn

Author

Paul Barry, Mar 16 2006

Status

approved