A049957 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) = 2, and a(3) = 3.

1, 2, 3, 8, 15, 37, 69, 137, 273, 682, 1296, 2560, 5098, 10189, 20373, 40745, 81489, 203722, 387072, 763960, 1522829, 3043120, 6084976, 12169338, 24338267, 48676398, 97352728, 194705424, 389410826, 778821645, 1557643285, 3115286569, 6230573137, 15576432842, 29595222400

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Crossrefs

Cf. A006257, A049933, A049937, A049945.

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, 3][n], s(n - 1) + a(2^ceil(log[2](n - 1)) + 2 - n)):
end proc:
seq(a(n), n = 1..34); # Petros Hadjicostas, Nov 11 2019

Extensions

Name edited by and more terms from Petros Hadjicostas, Nov 11 2019