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