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A130497 Repetition of odd numbers five times.

%I A130497 #32 Jan 29 2025 16:53:57
%S A130497 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,
%T A130497 13,13,13,13,15,15,15,15,15,17,17,17,17,17,19,19,19,19,19,21,21,21,21,
%U A130497 21,23,23,23,23,23,25,25,25,25,25,27,27,27,27,27,29,29,29,29,29,31,31,31
%N A130497 Repetition of odd numbers five times.
%H A130497 G. C. Greubel, <a href="/A130497/b130497.txt">Table of n, a(n) for n = 0..1000</a>
%H A130497 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,1,-1).
%F A130497 From _R. J. Mathar_, Mar 17 2010: (Start)
%F A130497 a(n) = a(n-1) + a(n-5) - a(n-6).
%F A130497 G.f.: (1+x)*(1-x+x^2-x^3+x^4)/((1+x+x^2+x^3+x^4) * (1-x)^2 ). (End)
%F A130497 a(n) = 2*floor(n/5)+1 = A130496(n)+1. - _Tani Akinari_, Jul 24 2013
%p A130497 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);
%t A130497 Flatten[Table[#,{5}]&/@Range[1,31,2]] (* _Harvey P. Dale_, Mar 27 2013~ *)
%o A130497 (PARI) my(x='x+O('x^80)); Vec((1+x^5)/((1-x)*(1-x^5))) \\ _G. C. Greubel_, Sep 12 2019
%o A130497 (Magma) R<x>:=PowerSeriesRing(Integers(), 80); Coefficients(R!( (1+x^5)/((1-x)*(1-x^5)) )); // _G. C. Greubel_, Sep 12 2019
%o A130497 (Sage)
%o A130497 def A130497_list(prec):
%o A130497     P.<x> = PowerSeriesRing(ZZ, prec)
%o A130497     return P((1+x^5)/((1-x)*(1-x^5))).list()
%o A130497 A130497_list(80) # _G. C. Greubel_, Sep 12 2019
%o A130497 (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
%Y A130497 Cf. A129756, A130496.
%K A130497 easy,nonn
%O A130497 0,6
%A A130497 _Paolo P. Lava_ and _Giorgio Balzarotti_, May 31 2007