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A050032
a(n) = a(n-1) + a(m) for n >= 4, where m = 2*n - 3 - 2^(p+1) and p is the unique value such that 2^p < n - 1 <= 2^(p+1), starting with a(1) = a(2) = 1 and a(3) = 3.
10
1, 1, 3, 4, 7, 8, 11, 18, 29, 30, 33, 40, 51, 80, 113, 164, 277, 278, 281, 288, 299, 328, 361, 412, 525, 802, 1083, 1382, 1743, 2268, 3351, 5094, 8445, 8446, 8449, 8456, 8467, 8496, 8529, 8580, 8693, 8970, 9251, 9550, 9911, 10436
OFFSET
1,3
LINKS
MAPLE
a := proc(n) option remember;
`if`(n < 4, [1, 1, 3][n], a(n - 1) + a(-2^ceil(log[2](n - 1)) + 2*n - 3)):
end proc:
seq(a(n), n = 1..60); # Petros Hadjicostas, Nov 14 2019
MATHEMATICA
Fold[Append[#1, #1[[-1]] + #1[[#2]]] &, {1, 1, 3}, Flatten@Table[2 k - 1, {n, 5}, {k, 2^n}]] (* Ivan Neretin, Sep 07 2015 *)
CROSSREFS
Similar sequences with different initial conditions are A050024 (1,1,1), A050028 (1,1,2), A050036 (1,1,4), A050040 (1,2,1), A050044 (1,2,2), A050048 (1,2,3), A050052 (1,2,4), A050056 (1,3,1), A050060 (1,3,2), A050064 (1,3,3), A050068 (1,3,4).
Sequence in context: A196923 A192051 A033195 * A330221 A343151 A014602
KEYWORD
nonn
EXTENSIONS
Name edited by Petros Hadjicostas, Nov 14 2019
STATUS
approved