

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
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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))^25]^25}/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(n1) + a(n5)  a(n6).
G.f.: (1+x)*(1x+x^2x^3+x^4)/((1+x+x^2+x^3+x^4) * (1x)^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))^25)^25', '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)/((1x)*(1x^5))) \\ G. C. Greubel, Sep 12 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 80); Coefficients(R!( (1+x^5)/((1x)*(1x^5)) )); // G. C. Greubel, Sep 12 2019
(Sage)
def A130497_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P((1+x^5)/((1x)*(1x^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[n1]+a[n5]a[n6]; 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



