A049934 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) = a(2) = a(3) = 1.

1, 1, 1, 4, 8, 16, 32, 64, 131, 259, 518, 1036, 2075, 4154, 8316, 16648, 33328, 66593, 133186, 266372, 532747, 1065498, 2131004, 4262024, 8524080, 17048227, 34096582, 68193423, 136387364, 272775767, 545553613, 1091111388, 2182231108

Offset

1,4

Links

Table of n, a(n) for n=1..33.

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, 1, 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, Apr 25 2020

Prog

(PARI) lista(nn) = { my(va = vector(nn)); va[1] = 1; va[2] = 1; va[3] = 1; 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)

Crossrefs

Cf. A049886 (similar, but with minus a(m)), A049887 (similar, but with minus a(2*m)), A049935 (similar, but with plus a(2*m)).

Sequence in context: A020707 A151821 A147639 * A328634 A089890 A338313

Adjacent sequences: A049931 A049932 A049933 * A049935 A049936 A049937

Keyword

nonn

Author

Clark Kimberling

Extensions

Name edited by Petros Hadjicostas, Apr 25 2020

Status

approved