

A049977


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


1



1, 3, 4, 11, 20, 50, 93, 185, 368, 920, 1748, 3453, 6876, 13743, 27479, 54957, 109912, 274780, 522082, 1030428, 2053989, 4104555, 8207405, 16413982, 32827412, 65654641, 131309190, 262618337, 525236644, 1050473279, 2100946551, 4201893101, 8403786200, 21009465500, 39917984450
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OFFSET

1,2


LINKS

Table of n, a(n) for n=1..35.


FORMULA

From Petros Hadjicostas, Nov 07 2019: (Start)
a(n) = a(2^ceiling(log_2(n1)) + 2  n) + Sum_{i = 1..n1} a(i) for n >= 4.
a(n) = a(n  1  A006257(n2)) + Sum_{i = 1..n1} a(i) for n >= 4. (End)


EXAMPLE

From Petros Hadjicostas, Nov 07 2019: (Start)
a(4) = a(2^ceiling(log_2(41)) + 2  4) + a(1) + a(2) + a(3) = a(2) + a(1) + a(2) + a(3) = 11.
a(5) = a(2^ceiling(log_2(51)) + 2  5) + a(1) + a(2) + a(3) + a(4) = a(1) + a(1) + a(2) + a(3) + a(4) = 20.
a(6) = a(2^ceiling(log_2(61)) + 2  6) + a(1) + a(2) + a(3) + a(4) + a(5) = a(4) + a(1) + a(2) + a(3) + a(4) + a(5) = 50.
a(7) = a(7  1  A006257(72)) + Sum_{i = 1..6} a(i) = a(3) + Sum_{i = 1..6} a(i) = 93.
a(8) = a(8  1  A006257(82)) + Sum_{i = 1..7} a(i) = a(2) + Sum_{i = 1..7} a(i) = 185. (End)


MAPLE

s := proc(n) option remember; `if`(n < 1, 0, a(n) + s(n  1)) end proc:
a := proc(n) option remember; `if`(n < 2, 1, `if`(n < 3, 3,
`if`(n < 4, 4, s(n  1) + a(Bits:Iff(n  2, n  2) + 3  n))))
end proc:
seq(a(n), n = 1 .. 40); # Petros Hadjicostas, Nov 07 2019


CROSSREFS

Cf. A006257, A049933, A049937, A049945.
Sequence in context: A036652 A295962 A097072 * A000677 A110865 A152982
Adjacent sequences: A049974 A049975 A049976 * A049978 A049979 A049980


KEYWORD

nonn


AUTHOR

Clark Kimberling


EXTENSIONS

Name edited by and more terms from Petros Hadjicostas, Nov 07 2019


STATUS

approved



