cp's OEIS Frontend

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.

%I A050032 #17 Nov 15 2019 03:29:14
%S A050032 1,1,3,4,7,8,11,18,29,30,33,40,51,80,113,164,277,278,281,288,299,328,
%T A050032 361,412,525,802,1083,1382,1743,2268,3351,5094,8445,8446,8449,8456,
%U A050032 8467,8496,8529,8580,8693,8970,9251,9550,9911,10436
%N 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.
%H A050032 Ivan Neretin, <a href="/A050032/b050032.txt">Table of n, a(n) for n = 1..8193</a>
%p A050032 a := proc(n) option remember;
%p A050032 `if`(n < 4, [1, 1, 3][n], a(n - 1) + a(-2^ceil(log[2](n - 1)) + 2*n - 3)):
%p A050032 end proc:
%p A050032 seq(a(n), n = 1..60); # _Petros Hadjicostas_, Nov 14 2019
%t A050032 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 *)
%Y A050032 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).
%K A050032 nonn
%O A050032 1,3
%A A050032 _Clark Kimberling_
%E A050032 Name edited by _Petros Hadjicostas_, Nov 14 2019