cp's OEIS Frontend

A050048 a(n) = a(n-1) + a(m) for n >= 3, 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 and a(2) = 2.

%I A050048 #19 Nov 15 2019 03:29:59
%S A050048 1,2,3,4,7,8,11,18,29,30,33,40,51,80,113,164,277,278,281,288,299,328,
%T A050048 361,412,525,802,1083,1382,1743,2268,3351,5094,8445,8446,8449,8456,
%U A050048 8467,8496,8529,8580,8693,8970,9251,9550,9911,10436
%N A050048 a(n) = a(n-1) + a(m) for n >= 3, 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 and a(2) = 2.
%C A050048 In the Mathematica program below, the author of the program uses the initial conditions a(1) = 1, a(2) = 2, and a(3) = 3. This is not necessary. We get the same sequence using the initial conditions a(1) = 1 and a(2) = 2. - _Petros Hadjicostas_, Nov 14 2019
%H A050048 Ivan Neretin, <a href="/A050048/b050048.txt">Table of n, a(n) for n = 1..8193</a>
%p A050048 a := proc(n) option remember;
%p A050048 `if`(n < 3, [1, 2][n], a(n - 1) + a(-2^ceil(log[2](n - 1)) + 2*n - 3)):
%p A050048 end proc:
%p A050048 seq(a(n), n = 1..60); # _Petros Hadjicostas_, Nov 14 2019
%t A050048 Fold[Append[#1, #1[[-1]] + #1[[#2]]] &, {1, 2, 3}, Flatten@Table[2 k - 1, {n, 5}, {k, 2^n}]] (* _Ivan Neretin_, Sep 07 2015 *)
%Y A050048 Cf. similar sequences with different initial conditions: A050024 (1,1,1), A050028 (1,1,2), A050032 (1,1,3), A050036 (1,1,4), A050040 (1,2,1), A050044 (1,2,2), A050052 (1,2,4), A050056 (1,3,1), A050060 (1,3,2), A050064 (1,3,3), A050068 (1,3,4).
%K A050048 nonn
%O A050048 1,2
%A A050048 _Clark Kimberling_
%E A050048 Name edited by _Petros Hadjicostas_, Nov 14 2019