cp's OEIS Frontend

A050034 a(n) = a(n-1) + a(m) for n >= 4, where m = n - 1 - 2^p 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) = 3.

%I A050034 #16 May 11 2020 02:29:49
%S A050034 1,1,3,4,5,6,7,10,14,15,16,19,23,28,34,41,51,52,53,56,60,65,71,78,88,
%T A050034 102,117,133,152,175,203,237,278,279,280,283,287,292,298,305,315,329,
%U A050034 344,360,379,402,430,464
%N A050034 a(n) = a(n-1) + a(m) for n >= 4, where m = n - 1 - 2^p 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) = 3.
%H A050034 Ivan Neretin, <a href="/A050034/b050034.txt">Table of n, a(n) for n = 1..8193</a>
%t A050034 Fold[Append[#1, #1[[-1]] + #1[[#2]]] &, {1, 1, 3}, Flatten@Table[k, {n, 5}, {k, 2^n}]] (* _Ivan Neretin_, Sep 08 2015 *)
%o A050034 (PARI) lista(nn) = {nn = max(nn, 3); my(va = vector(nn)); va[1] = 1; va[2] = 1; va[3] = 3; for(n=4, nn, va[n] = va[n-1] + va[n - 1 - 2^logint(n-2, 2)]); va; } \\ _Petros Hadjicostas_, May 10 2020
%Y A050034 Cf. similar sequences with different initial conditions: A050026 (1,1,1); A050030 (1,1,2);  this sequence (1,1,3); A050038 (1,1,4); A050042 (1,2,1); A050046 (1,2,2); A050050 (1,2,3); A050054 (1,2,4); A050058 (1,3,1); A050062 (1,3,2); A050066 (1,3,3); A050070 (1,3,4).
%K A050034 nonn
%O A050034 1,3
%A A050034 _Clark Kimberling_
%E A050034 Name edited by _Petros Hadjicostas_, May 10 2020