A214126 - OEIS

%I #19 May 21 2021 16:24:11

%S 1,1,2,2,3,2,4,3,5,2,5,4,6,3,7,5,8,2,7,5,7,4,9,6,10,3,9,7,10,5,12,8,

%T 13,2,10,7,9,5,12,7,12,4,11,9,13,6,15,10,16,3,13,9,12,7,16,10,17,5,15,

%U 12,17,8,20,13,21,2,15,10,12,7,17,9,16,5,14,12

%N a(2n)=a(n-1)+a(n) and a(2n+1)=a(n+1) for n>=1, with a(0)=a(1)=1.

%C a(2^n) = A000045(n+2), a(2^n-1) = A000045(n+1). - _Alois P. Heinz_, Jul 06 2012

%H Alois P. Heinz, <a href="/A214126/b214126.txt">Table of n, a(n) for n = 0..8192</a>

%F a(0) = a(1) = 1, for n>=1:  a(2*n) = a(n-1)+a(n) and a(2*n+1) = a(n+1).

%e a(2^n+1) = 2 because a(2) = 2 and a(2*n+1) = a(n+1).

%p a:= proc(n) local r;

%p       a(n):= `if`(n<2, 1, `if`(irem(n, 2, 'r')=0, a(r-1)+a(r), a(r+1)))

%p     end:

%p seq(a(n), n=1..100);  # _Alois P. Heinz_, Jul 06 2012

%t a[0] = a[1] = 1;

%t a[n_] := a[n] = If[EvenQ[n], a[n/2-1] + a[n/2], a[(n-1)/2+1]];

%t Array[a, 100, 0] (* _Jean-François Alcover_, May 31 2019 *)

%o (Python)

%o a = [1]*(77*2)

%o for n in range(1,77):

%o     a[2*n  ]=a[n-1]+a[n]

%o     a[2*n+1]=a[n+1]

%o     print(str(a[n-1]),end=',')

%Y Cf. A120562: same formula, seed {0,1}, first term removed.

%Y Cf. A082498: same formula, seed {1,0}, first term removed.

%Y Cf. A214127: same formula, seed {1,2}.

%Y Cf. A000045.

%K nonn,easy

%O 0,3

%A _Alex Ratushnyak_, Jul 04 2012