login
a(8n)=n, a(8n+4)=a(8n)+a(8n+8), a(4n+2)=a(4n)+a(4n+4), a(2n+1)=a(2n)+a(2n+2).
1

%I #14 Sep 08 2022 08:44:49

%S 0,1,1,2,1,3,2,3,1,5,4,7,3,8,5,7,2,9,7,12,5,13,8,11,3,13,10,17,7,18,

%T 11,15,4,17,13,22,9,23,14,19,5,21,16,27,11,28,17,23,6,25,19,32,13,33,

%U 20,27,7,29,22,37,15,38,23,31,8,33,25,42,17,43,26,35,9,37,28,47,19,48,29,39,10

%N a(8n)=n, a(8n+4)=a(8n)+a(8n+8), a(4n+2)=a(4n)+a(4n+4), a(2n+1)=a(2n)+a(2n+2).

%H G. C. Greubel, <a href="/A026730/b026730.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_16">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,-1).

%F a(n) = 2*a(n-8) - a(n-16).

%F G.f.: x*(1 + x + x^2)*(1 + x^2 + x^4)*(1 + x^4 + x^8)/(1 - x^8)^2. - _G. C. Greubel_, Oct 26 2019

%p seq(coeff(series(x*(1+x+x^2)*(1+x^2+x^4)*(1+x^4+x^8)/(1-x^8)^2, x, n+1), x, n), n = 0 .. 90); # _G. C. Greubel_, Oct 26 2019

%t LinearRecurrence[{0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,-1}, {0,1,1,2,1,3,2,3,1, 5,4,7,3,8,5,7},90] (* _Harvey P. Dale_, May 10 2012 *)

%t CoefficientList[Series[x*(1+x+x^2)*(1+x^2+x^4)*(1+x^4+x^8)/(1-x^8)^2, {x, 0, 90}], x]

%o (PARI) my(x='x+O('x^90)); concat([0], Vec(x*(1+x+x^2)*(1+x^2+x^4)*(1+x^4+x^8)/(1-x^8)^2)) \\ _G. C. Greubel_, Oct 26 2019

%o (Magma) R<x>:=PowerSeriesRing(Integers(), 90); [0] cat Coefficients(R!( x*(1+x+x^2)*(1+x^2+x^4)*(1+x^4+x^8)/(1-x^8)^2 )); // _G. C. Greubel_, Oct 26 2019

%o (Sage)

%o def A026730_list(prec):

%o P.<x> = PowerSeriesRing(ZZ, prec)

%o return P( x*(1+x+x^2)*(1+x^2+x^4)*(1+x^4+x^8)/(1-x^8)^2 ).list()

%o A026730_list(90) # _G. C. Greubel_, Oct 26 2019

%o (GAP) a:=[0,1,1,2,1,3,2,3,1,5,4,7,3,8,5,7];; for n in [17..90] do a[n]:=2*a[n-8]-a[n-16]; od; a; # _G. C. Greubel_, Oct 26 2019

%K nonn,easy

%O 0,4

%A J. Carl Bellinger (carlb(AT)ctron.com)

%E Shorter description and more terms from _David W. Wilson_