A306622 - OEIS

%I #28 Mar 16 2022 19:01:25

%S 1,1,1,2,3,5,8,16,29,53,98,180,331,609,1120,2240,4300,8269,15929,

%T 30738,59236,114172,220075,424221,817704,1576172,3038172,5856269,

%U 11288317,21758930,41941688,83883376,164728580,323600891,635913465,1250068000,2458194312,4832505248,9500281916

%N a(1) = 1, for n >= 2, a(n) = Sum_{i=1..floor(log_2(n))} a(n-i).

%H Michael De Vlieger, <a href="/A306622/b306622.txt">Table of n, a(n) for n = 1..3332</a>

%F For n >= 2 a(2^n) = 2*a((2^n)-1).

%e n = 7, floor(log_2(7)) = 2, a(7) = a(7-1) + a(7-2) = a(6) + a(5).

%t a[1] = 1; a[n_] := a[n] = Total@ Map[a[n - #] &, Range[Floor@ Log2[n]]]; Array[a, 39] (* _Michael De Vlieger_, Mar 16 2022 *)

%o (PARI) lista(nn) = {my(va = vector(nn)); va[1] = 1; for (n=2, nn, va[n] = sum(i=1, log(n)\log(2), va[n-i]);); va;} \\ _Michel Marcus_, Mar 04 2019

%Y Cf. A000523.

%K nonn

%O 1,4

%A _Ctibor O. Zizka_, Mar 01 2019

%E More terms from _Michel Marcus_, Mar 16 2022