A049893 -id:A049893 - cp's OEIS frontend

A049897 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) = a(2) = 1 and a(3) = 4.

1, 1, 4, 5, 10, 16, 33, 69, 138, 208, 452, 921, 1848, 3701, 7403, 14809, 29618, 44428, 96262, 196226, 394305, 789537, 1579543, 3159330, 6318730, 12637529, 25275094, 50550205, 101100416, 202200837, 404401675, 808803353, 1617606706

Offset: 1

Clark Kimberling

nonn

Cf. A049885, A049893, A049913, A049917, A049921.

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, 4][n], s(n - 1) - a(2^ceil(log[2](n - 1)) + 2 - n)):
end proc:
seq(a(n), n = 1..40); # Petros Hadjicostas, Nov 14 2019

Name edited by Petros Hadjicostas, Nov 14 2019

A049901 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) = 1.

Original entry on oeis.org

1, 2, 1, 2, 5, 9, 19, 37, 75, 114, 246, 502, 1008, 2019, 4039, 8077, 16155, 24234, 52506, 107032, 215075, 430656, 861568, 1723268, 3446575, 6893188, 13786394, 27572798, 55145600, 110291203, 220582407, 441164813, 882329627, 1323494442

Offset: 1

Clark Kimberling

nonn

Cf. A049885, A049893, A049913, A049917, A049921.

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, 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 14 2019

Name edited by Petros Hadjicostas, Nov 14 2019

cp's OEIS Frontend

A049897 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) = a(2) = 1 and a(3) = 4.

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