A260956 a(0)=1; a(n) = Sum_{k=1..n-1} d(k)*a(n-k), where d(m) is m-th bit in binary expansion of n.

1, 1, 1, 2, 2, 3, 5, 10, 10, 13, 23, 43, 66, 122, 231, 462, 462, 528, 759, 1452, 1980, 3201, 5412, 9603, 15015, 26598, 47025, 88638, 162261, 312939, 610863, 1221726, 1221726, 1310364, 1623303, 2547105, 3768831, 6300921, 9234588, 14715360, 21016281, 32797974

Offset: 0

Author

Anders Hellström, Sep 10 2015

Keywords

• nonn
• base

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..4575 (terms n = 1..1000 from Anders Hellström)

Crossrefs

Cf. A007088, A000120, A323355.

Cf. A033639 (when binary digits are taken in the reverse order).

Programs

Maple

a:= proc(n) option remember; `if`(n=0, 1, (l-> add(
      a(n-i)*l[-i], i=1..nops(l)))(convert(n, base, 2)))
    end:
seq(a(n), n=0..50);  # Alois P. Heinz, Jan 18 2019

Mathematica

a[0] = 1; a[n_] := a[n] = Total[(d = IntegerDigits[n, 2]) * Table[a[n - k], {k, 1, Length[d]}]]; Array[a, 50, 0] (* Amiram Eldar, Jul 25 2023 *)

PARI

first(m)=my(v=vector(m));v[1]=1;v[2]=1;for(i=3,m,v[i]=0;d=digits(i,2);for(j=1,#d,v[i]+=d[j]*v[i-j]));v

PARI

lista(nn) = {my(va = vector(nn), vb); va[1] = 1; for (n=2, nn, vb = binary(n); va[n] = sum(k=1, #vb, vb[k]*(if (n==k, 1, va[n-k])));); concat(1, va);} \\ Michel Marcus, Jan 12 2019

Extensions

a(0)=1 prepended by Alois P. Heinz, Jan 18 2019