A326816 a(0) = 0, a(1) = 1, and for n > 1, a(n) = Sum_{k = 0..n} a((n-k) AND k) (where AND denotes the bitwise AND operator).

0, 1, 1, 0, 3, 2, 2, 0, 9, 10, 10, 12, 12, 8, 4, 0, 27, 38, 46, 60, 66, 68, 72, 72, 90, 84, 76, 72, 44, 24, 8, 0, 81, 130, 182, 228, 302, 332, 384, 360, 526, 572, 636, 600, 624, 576, 568, 432, 764, 888, 996, 1008, 972, 936, 888, 864, 712, 560, 408, 320, 144

Offset

0,5

Comments

This sequence combines features of A006581 and of A007461.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..8191

Formula

a(n) is odd iff n is a power of 2.

a(n) = 0 iff n = 2^k with k = 0 or k = 2.

a(2^k) = 3^(k-1) for any k > 0.

a(2^k+1) = A056182(k-1) for any k > 1.

Example

a(2) = a(2 AND 0) + a(1 AND 1) + a(0 AND 2) = a(0) + a(1) + a(0) = 1.

Maple

a:= proc(n) option remember; `if`(n<2, n,
      add(a(Bits[And](n-k, k)), k=0..n))
    end:
seq(a(n), n=0..80);  # Alois P. Heinz, Oct 20 2019

Prog

(PARI) a = vector(61); for (n=0, #a-1, print1 (a[1+n] = if (n==0, 0, n==1, 1, sum (k=0, n, a[1+bitand(n-k, k)])) ", "))

Crossrefs

Cf. A006581, A007461, A056182.

Sequence in context: A326152 A308181 A361862 * A323557 A155917 A291770

Adjacent sequences: A326813 A326814 A326815 * A326817 A326818 A326819

Keyword

nonn,look,base

Author

Rémy Sigrist, Oct 20 2019

Status

approved