A049902 a(n) = a(1) + a(2) + ... + a(n-1) - a(m) for n >= 4, where m = n - 1 - 2^p and p is the unique integer such that 2^p < n - 1 <= 2^(p+1), starting with a(1) = 1, a(2) = 2, and a(3) = 1.

1, 2, 1, 3, 5, 11, 21, 43, 84, 170, 339, 679, 1356, 2710, 5414, 10818, 21614, 43270, 86539, 173079, 346156, 692310, 1384614, 2769218, 5538414, 11076787, 22153488, 44306807, 88613274, 177225871, 354450388, 708898072, 1417790740

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Programs

Maple

s := proc(n) option remember; `if`(n < 1, 0, a(n) + s(n - 1)) end proc:
a := proc(n) option remember;
`if`(n < 4, [1, 2, 1][n], s(n - 1) - a(-2^ceil(-1 + log[2](n - 1)) + n - 1)):
end proc:
seq(a(n), n = 1..40); # Petros Hadjicostas, Nov 19 2019

Extensions

Name edited by Petros Hadjicostas, Nov 19 2019