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

0,4

Links

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

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 *)

Prog

(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

Crossrefs

Cf. A007088, A000120, A323355.

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

Sequence in context: A374735 A208437 A130377 * A360299 A344708 A322113

Adjacent sequences: A260953 A260954 A260955 * A260957 A260958 A260959

Keyword

nonn,base

Author

Anders Hellström, Sep 10 2015

Extensions

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

Status

approved