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
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