A297621 a(0) = 1; for n > 0, a(n) = 1 + Sum_{k = 1..n} 2^k a(floor(log_2(k))).

1, 3, 15, 39, 279, 759, 1719, 3639, 13623, 33591, 73527, 153399, 313143, 632631, 1271607, 2549559, 20834103, 57403191, 130541367, 276817719, 569370423, 1154475831, 2324686647, 4665108279, 9345951543, 18707638071, 37431011127, 74877757239, 149771249463

Offset

0,2

Links

Robert P. Adkins, Table of n, a(n) for n = 0..999

Robert Adkins, Can you find an explicit formula for the runtime recursion of T(n) ..., Quora.

Mathematica

a[0] := 1; a[n_] := a[n] = 1 + Sum[2^k a[Floor@ Log2@ k], {k, 1, n}]; Array[a[#] &, 28, 0] (* Michael De Vlieger, Jan 02 2018 *)

Prog

(Python)
from math import log
def exp_fit(n, a, b):
    k = int(log(n, 2))
    return 3 * (a[k] * (2 ** (n + 1)) - b[k])
def S(n):
    if n == 0:
        return 1
    k = int(log(n, 2))
    a = [0]
    b = [-1]
    for i in range(1, k + 1):
        S_0 = exp_fit(i, a, b)
        S_1 = exp_fit(2 ** i - 1, a, b)
        a.append(S_0 / 3)
        b.append(((2 ** 2 ** i) * S_0 - S_1) / 3)
    return exp_fit(n, a, b)

Crossrefs

Sequence in context: A318738 A146853 A183476 * A014309 A298049 A298884

Adjacent sequences: A297618 A297619 A297620 * A297622 A297623 A297624

Keyword

nonn

Author

Robert P. Adkins, Jan 01 2018

Status

approved