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A116529 a(2*n + 1) = a(n), a(2*n + 2) = 2*a(n) + a(n-1).

%I A116529 #25 Dec 19 2024 11:46:19
%S A116529 1,1,2,1,3,2,5,1,4,3,7,2,7,5,12,1,7,4,9,3,10,7,17,2,11,7,16,5,17,12,
%T A116529 29,1,14,7,15,4,15,9,22,3,15,10,23,7,24,17,41,2,21,11,24,7,25,16,39,5,
%U A116529 26,17,39,12,41,29,70,1,31,14,29,7,28,15
%N A116529 a(2*n + 1) = a(n), a(2*n + 2) = 2*a(n) + a(n-1).
%H A116529 G. C. Greubel, <a href="/A116529/b116529.txt">Table of n, a(n) for n = 0..2500</a>
%H A116529 Kevin Ryde, <a href="/A116529/a116529.gp.txt">PARI/GP Code</a>
%F A116529 From _G. C. Greubel_, Oct 30 2016: (Start)
%F A116529 a(2*n + 1) = a(n), n>=1.
%F A116529 a(2*n + 2) = 2*a(n) + a(n-1), n>=1. (End)
%F A116529 G.f. g(x) satisfies g(x) = 1 + (x^4+2*x^2+x)*g(x^2). - _Robert Israel_, Nov 13 2017
%p A116529 gg:= 1:
%p A116529 for iter from 1 to 7 do
%p A116529   gg:= convert(series(1+(x^4+2*x^2+x)*eval(gg,x=x^2), x, 2^iter+1),polynom)
%p A116529 od:
%p A116529 seq(coeff(gg,x,n),n=0..2^7); # _Robert Israel_, Nov 13 2017
%t A116529 b[0] := 0; b[1] := 1;
%t A116529 b[n_?EvenQ] := b[n] = b[n/2];
%t A116529 b[n_?OddQ] := b[n] = 2*b[(n - 1)/2] + b[(n - 3)/2];
%t A116529 Table[b[n], {n, 1, 70}]
%o A116529 (PARI) \\ See links.
%Y A116529 Cf. A116528, A116552, A116553, A116554, A116555.
%K A116529 nonn,easy
%O A116529 0,3
%A A116529 _Roger L. Bagula_, Mar 15 2006
%E A116529 New name using formula, _Joerg Arndt_, Dec 17 2022