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

Author

Paolo P. Lava and Giorgio Balzarotti, May 31 2007

Keywords

• easy
• nonn

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).

Crossrefs

Cf. A129756, A130496.

Programs

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

Magma

R:=PowerSeriesRing(Integers(), 80); Coefficients(R!( (1+x^5)/((1-x)*(1-x^5)) )); // G. C. Greubel, Sep 12 2019

Maple

P:=proc(q) local k,n; k:=[]; for n from 0 to q do k:=[op(k),2*floor(n/5)+1]; od; op(k); end: P(77);

Mathematica

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

PARI

my(x='x+O('x^80)); Vec((1+x^5)/((1-x)*(1-x^5))) \\ G. C. Greubel, Sep 12 2019

Sage

def A130497_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P((1+x^5)/((1-x)*(1-x^5))).list()
A130497_list(80) # G. C. Greubel, Sep 12 2019

Formula

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