A049900 a(n) = a(1) + a(2) + ... + a(n-1) - a(m) for n >= 4, where m = 2*n - 3 - 2^(p+1) 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.

1, 2, 1, 3, 6, 12, 24, 43, 68, 159, 318, 631, 1244, 2444, 4638, 8350, 13306, 31249, 62498, 124991, 249964, 499884, 999518, 1998110, 3992826, 7976984, 15904776, 31622086, 62494618, 121995928, 232079906, 417569970, 665554652, 1563189209, 3126378418, 6252756831, 12505513644

Offset

1,2

Links

Michael De Vlieger, Table of n, a(n) for n = 1..3327

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, 1][n], s(n - 1) - a(-2^ceil(log[2](n - 1)) + 2*n - 3)):
end proc:
seq(a(n), n = 1..40); # Petros Hadjicostas, Nov 15 2019

Mathematica

Nest[Append[#1, Total@ #1 - #1[[2 #2 - 3 - 2^Ceiling@ Log2[#2 - 1]]]] & @@ {#, Length@ # + 1} &, {1, 2, 1}, 34] (* Michael De Vlieger, Nov 19 2019 *)

Prog

(PARI) lista(nn) = {my(va = vector(nn), s); va[1] = 1; va[2] = 2; va[3] = 1; s = sum(k=1, 3, va[k]); for (n=4, nn, va[n] = s - va[2*n - 3 - 2^ceil(log(n-1)/log(2))]; s += va[n]; ); va; } \\ Michel Marcus, Nov 20 2019

Crossrefs

Sequence in context: A357844 A104529 A095024 * A024741 A024961 A260666

Adjacent sequences: A049897 A049898 A049899 * A049901 A049902 A049903

Keyword

nonn

Author

Clark Kimberling

Extensions

Name edited by and more terms from Petros Hadjicostas, Nov 15 2019

Status

approved