A372205 a(n) = (-1)^n*a((n - 2^A007814(n))/2) + a(floor((2*n - 2^A007814(n))/2)) for n > 0 and a(0) = 1.

1, 0, 1, 1, 2, 1, 2, 1, 3, 1, 3, 2, 5, 3, 5, 4, 4, 1, 4, 3, 7, 4, 7, 5, 10, 5, 10, 7, 15, 10, 15, 11, 5, 1, 5, 4, 9, 5, 9, 6, 13, 6, 13, 9, 20, 13, 20, 15, 17, 7, 17, 12, 27, 17, 27, 20, 37, 22, 37, 27, 52, 37, 52, 41, 6, 1, 6, 5, 11, 6, 11, 7, 16, 7, 16, 11, 25, 16, 25, 19

Offset: 0

Author

Peter Luschny, Apr 22 2024

Keywords

• nonn

Comments

This sequence was originally introduced by Mikhail Kurkov in A217924 where he conjectured that A217924(n) = Sum_{k=0..2^n-1} a(k).

Crossrefs

Cf. A007814, A000296, A217924, A288268.

Programs

Maple

f := n -> padic[ordp](n, 2):
a := proc(n) option remember; if n = 0 then return 1 fi;
(-1)^n*a((n - 2^f(n))/2) + a(floor((2*n - 2^f(n))/2)) end:
seq(a(n), n = 0..79);

Formula

Conjecture (by Mikhail Kurkov): a(2^n - 1) = A000296(n).

Conjecture (by Mikhail Kurkov): a((4^n - 1)/3) = A288268(n).