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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.

%I A260956 #29 Jul 25 2023 04:04:35
%S A260956 1,1,1,2,2,3,5,10,10,13,23,43,66,122,231,462,462,528,759,1452,1980,
%T A260956 3201,5412,9603,15015,26598,47025,88638,162261,312939,610863,1221726,
%U A260956 1221726,1310364,1623303,2547105,3768831,6300921,9234588,14715360,21016281,32797974
%N 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.
%H A260956 Alois P. Heinz, <a href="/A260956/b260956.txt">Table of n, a(n) for n = 0..4575</a> (terms n = 1..1000 from Anders Hellström)
%p A260956 a:= proc(n) option remember; `if`(n=0, 1, (l-> add(
%p A260956       a(n-i)*l[-i], i=1..nops(l)))(convert(n, base, 2)))
%p A260956     end:
%p A260956 seq(a(n), n=0..50);  # _Alois P. Heinz_, Jan 18 2019
%t A260956 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 *)
%o A260956 (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
%o A260956 (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
%Y A260956 Cf. A007088, A000120, A323355.
%Y A260956 Cf. A033639 (when binary digits are taken in the reverse order).
%K A260956 nonn,base
%O A260956 0,4
%A A260956 _Anders Hellström_, Sep 10 2015
%E A260956 a(0)=1 prepended by _Alois P. Heinz_, Jan 18 2019