

A049963


a(n) = a(1) + a(2) + ... + a(n1) + a(m) for n >= 4, where m = 2*n  2  2^(p+1) and p is the unique integer such that 2^p < n1 <= 2^(p+1), with a(1) = 1, a(2) = 2 and a(3) = 4.


3



1, 2, 4, 9, 25, 43, 93, 220, 617, 1016, 2039, 4112, 8401, 17598, 38292, 90070, 252612, 415156, 830319, 1660672, 3321521, 6643838, 13290772, 26595030, 53262532, 106850150, 214945816, 434874798, 889700788, 1859656696
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

The number m in the definition of the sequence equals 2*n  2  x, where x is the smallest power of 2 >= n1. It turns out that m = 1 + A006257(n2), where the sequence b(n) = A006257(n) satisfies b(2*n) = 2*b(n)  1 and b(2*n + 1) = 2*b(n) + 1, and it is related to the socalled Josephus's problem.  Petros Hadjicostas, Sep 25 2019


LINKS

Table of n, a(n) for n=1..30.
Index entries for sequences related to the Josephus Problem


FORMULA

a(n) = a(1 + A006257(n2)) + Sum_{i = 1..n1} a(i) for n >= 4 with a(1) = 1, a(2) = 2 and a(3) = 4.  Petros Hadjicostas, Sep 25 2019


EXAMPLE

From Petros Hadjicostas, Sep 25 2019: (Start)
a(4) = a(1 + A006257(42)) + a(1) + a(2) + a(3) = a(2) + a(1) + a(2) + a(3) = 9.
a(7) = a(1 + A006257(72)) + a(1) + a(2) + a(3) + a(4) + a(5) + a(6) = a(4) + a(1) + a(2) + a(3) + a(4) + a(5) + a(6) = 93.
(End)


MAPLE

a := proc(n) local i; option remember; if n < 4 then return [1, 2, 4][n]; end if; add(a(i), i = 1 .. n  1) + a(2*n  3  Bits:Iff(n  2, n  2)); end proc;
seq(a(n), n = 1..40); # Petros Hadjicostas, Sep 25 2019, courtesy of Peter Luschny


CROSSREFS

Cf. A006257, A049920, A049939, A049960, A049964, A049979.
Cf. A049914 (similar, but with minus a(m/2)), A049915 (similar, but with minus a(m)), A049962 (similar, but with plus a(m/2)).
Sequence in context: A013091 A013168 A013183 * A114110 A337693 A335342
Adjacent sequences: A049960 A049961 A049962 * A049964 A049965 A049966


KEYWORD

nonn


AUTHOR

Clark Kimberling


EXTENSIONS

Name edited by Petros Hadjicostas, Sep 25 2019


STATUS

approved



