A130497 Repetition of odd numbers five times.

1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 7, 7, 7, 7, 7, 9, 9, 9, 9, 9, 11, 11, 11, 11, 11, 13, 13, 13, 13, 13, 15, 15, 15, 15, 15, 17, 17, 17, 17, 17, 19, 19, 19, 19, 19, 21, 21, 21, 21, 21, 23, 23, 23, 23, 23, 25, 25, 25, 25, 25, 27, 27, 27, 27, 27, 29, 29, 29, 29, 29, 31, 31, 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) = -1 + 2*Sum_{k=0..n} {[8*(sin(2*Pi*k/5))^2-5]^2-5}/20, with n>=0.

a(n) = -1 + (1/25)*Sum_{k=0..n} ( (-9*[k mod 5] +[(k+1) mod 5] +[(k+2) mod 5] +[(k+3) mod 5] +11*[(k+4) mod 5]) ), with n>=0.

a(n) = -1 + 2*Sum{k=0..n} (1 - (k^4 mod 5) ), with n>=0. - Paolo P. Lava, Feb 17 2010

From R. J. Mathar, Mar 17 2010: (Start)

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

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

a(n) = 2*floor(n/5)+1 = A130496(n)+1. - Tani Akinari, Jul 24 2013

Maple

P:=proc(n) local i, j, k; for i from 0 by 1 to n do j:=-1+2*sum('(8*(sin(2*Pi*k/5))^2-5)^2-5', 'k'=0..i)/20 ; print(j); od; end: P(100);

Mathematica

Flatten[Table[#, {5}]&/@Range[1, 31, 2]] (* Harvey P. Dale, Mar 27 2013~ *)

Prog

(PARI) my(x='x+O('x^80)); Vec((1+x^5)/((1-x)*(1-x^5))) \\ G. C. Greubel, Sep 12 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 80); Coefficients(R!( (1+x^5)/((1-x)*(1-x^5)) )); // G. C. Greubel, Sep 12 2019
(Sage)
def A130497_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P((1+x^5)/((1-x)*(1-x^5))).list()
A130497_list(80) # G. C. Greubel, Sep 12 2019
(GAP) a:=[1, 1, 1, 1, 1, 3];; for n in [7..80] do a[n]:=a[n-1]+a[n-5]-a[n-6]; od; a; # G. C. Greubel, Sep 12 2019

Crossrefs

Cf. A129756.

Sequence in context: A204854 A113215 A105591 * A178154 A270774 A263144

Adjacent sequences: A130494 A130495 A130496 * A130498 A130499 A130500

Keyword

easy,nonn

Author

Paolo P. Lava and Giorgio Balzarotti, May 31 2007

Extensions

Corrected formula by Paolo P. Lava, Feb 17 2010

Status

approved