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

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, 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, 26, 17, 39, 12, 41, 29, 70, 1, 31, 14, 29, 7, 28, 15

Offset: 0

Author

Roger L. Bagula, Mar 15 2006

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..2500
• Kevin Ryde, PARI/GP Code

Crossrefs

Cf. A116528, A116552, A116553, A116554, A116555.

Programs

Maple

gg:= 1:
for iter from 1 to 7 do
  gg:= convert(series(1+(x^4+2*x^2+x)*eval(gg,x=x^2), x, 2^iter+1),polynom)
od:
seq(coeff(gg,x,n),n=0..2^7); # Robert Israel, Nov 13 2017

Mathematica

b[0] := 0; b[1] := 1;
b[n_?EvenQ] := b[n] = b[n/2];
b[n_?OddQ] := b[n] = 2*b[(n - 1)/2] + b[(n - 3)/2];
Table[b[n], {n, 1, 70}]

PARI

\\ See links.

Formula

From G. C. Greubel, Oct 30 2016: (Start)

a(2*n + 1) = a(n), n>=1.

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

G.f. g(x) satisfies g(x) = 1 + (x^4+2*x^2+x)*g(x^2). - Robert Israel, Nov 13 2017

Extensions

New name using formula, Joerg Arndt, Dec 17 2022