A049917 a(n) = a(1) + a(2) + ... + a(n-1) - 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), starting with a(1) = 1, a(2) = 3, and a(3) = 1.

1, 3, 1, 2, 6, 11, 23, 44, 90, 137, 295, 602, 1209, 2422, 4845, 9688, 19378, 29069, 62981, 128385, 257983, 516573, 1033453, 2067064, 4134175, 8268396, 16536813, 33073638, 66147281, 132294566, 264589133, 529178264, 1058356530

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, 3, 1][n], s(n - 1) - a(2^ceil(log[2](n - 1)) + 2 - n)):
end proc:
seq(a(n), n = 1..40); # Petros Hadjicostas, Nov 12 2019

Extensions

Name edited by Petros Hadjicostas, Nov 12 2019