A049935 a(n) = a(1) + a(2) + ... + a(n-1) + a(m) for n >= 4, where m = 2*n - 2 - 2^(p+1) 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, 11, 19, 41, 97, 272, 448, 899, 1813, 3704, 7759, 16883, 39712, 111377, 183043, 366089, 732193, 1464464, 2929279, 5859923, 11725792, 23483537, 47110405, 94769960, 191737006, 392270525, 819925663, 1784477927, 4197144511

Offset

1,4

Links

Table of n, a(n) for n=1..32.

Formula

a(n) = (1/2)*A049959(n) for n > 3. - Petros Hadjicostas, Apr 27 2020

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(log[2](n - 1)) + 2*n - 2)):
end proc:
seq(a(n), n = 1..40); \\ Petros Hadjicostas, Apr 25 2020

Crossrefs

Cf. A049886 (similar, but with minus a(m/2)), A049887 (similar, but with minus a(m)), A049934 (similar, but with plus a(m)), A049959.

Sequence in context: A038431 A009908 A321643 * A074973 A327457 A025526

Adjacent sequences: A049932 A049933 A049934 * A049936 A049937 A049938

Keyword

nonn

Author

Clark Kimberling

Extensions

Name edited by Petros Hadjicostas, Apr 25 2020

Status

approved