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

Author

Rémy Sigrist, Oct 20 2019

Keywords

• nonn
• look
• base

Comments

This sequence combines features of A006581 and of A007461.

Examples

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

Links

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

Crossrefs

Cf. A006581, A007461, A056182.

Programs

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

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)])) ", "))

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.