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A130497 Repetition of odd numbers five times. 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 28 18:51 EST 2022. Contains 358421 sequences. (Running on oeis4.)