A306622 a(1) = 1, for n >= 2, a(n) = Sum_{i=1..floor(log_2(n))} a(n-i).

1, 1, 1, 2, 3, 5, 8, 16, 29, 53, 98, 180, 331, 609, 1120, 2240, 4300, 8269, 15929, 30738, 59236, 114172, 220075, 424221, 817704, 1576172, 3038172, 5856269, 11288317, 21758930, 41941688, 83883376, 164728580, 323600891, 635913465, 1250068000, 2458194312, 4832505248, 9500281916

Offset

1,4

Links

Michael De Vlieger, Table of n, a(n) for n = 1..3332

Formula

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A000523.

Sequence in context: A192645 A050295 A121649 * A030034 A370002 A308852

Adjacent sequences: A306619 A306620 A306621 * A306623 A306624 A306625

Keyword

nonn

Author

Ctibor O. Zizka, Mar 01 2019

Extensions

More terms from Michel Marcus, Mar 16 2022

Status

approved