A049962 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) = 4.

1, 2, 4, 8, 17, 33, 67, 136, 276, 545, 1091, 2184, 4372, 8753, 17522, 35078, 70225, 140315, 280631, 561264, 1122532, 2245073, 4490162, 8980358, 17960785, 35921710, 71843689, 143687924, 287376941, 574756070, 1149516521, 2299041811

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Crossrefs

Cf. A049914 (similar, but with minus a(m)), A049915 (similar, but with minus a(2*m)), A049963 (similar, but with plus a(2*m)).

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, 4][n], s(n - 1) + a(-2^ceil(log[2](n - 1) - 1) + n - 1)); end proc;
seq(a(n), n = 1 .. 40); # Petros Hadjicostas, Apr 23 2020

PARI

lista(nn) = { my(va = vector(nn)); va[1] = 1; va[2] = 2; va[3] = 4; my(sa = vecsum(va)); for (n=4, nn, va[n] = sa + va[n - 1 - 2^ceil(-1 + log(n-1)/log(2))]; sa += va[n]; ); va; } \\ Petros Hadjicostas, Apr 26 2020 (with nn > 2).

Extensions

Name edited by Petros Hadjicostas, Apr 23 2020