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A297621
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a(0) = 1; for n > 0, a(n) = 1 + Sum_{k = 1..n} 2^k a(floor(log_2(k))).
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1
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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
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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LINKS
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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.
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MATHEMATICA
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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 *)
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PROG
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(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)
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CROSSREFS
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Sequence in context: A318738 A146853 A183476 * A014309 A298049 A298884
Adjacent sequences: A297618 A297619 A297620 * A297622 A297623 A297624
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KEYWORD
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nonn
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AUTHOR
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Robert P. Adkins, Jan 01 2018
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STATUS
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approved
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