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A050036 a(n) = a(n-1) + a(m) for n >= 4, where m = 2*n - 3 - 2^(p+1) and 2^p < n - 1 <= 2^(p+1), starting with a(1) = a(2) = 1 and a(3) = 4.

%I A050036 #17 Nov 15 2019 03:29:22
%S A050036 1,1,4,5,9,10,14,23,37,38,42,51,65,102,144,209,353,354,358,367,381,
%T A050036 418,460,525,669,1022,1380,1761,2221,2890,4270,6491,10761,10762,10766,
%U A050036 10775,10789,10826,10868,10933,11077,11430,11788
%N A050036 a(n) = a(n-1) + a(m) for n >= 4, where m = 2*n - 3 - 2^(p+1) and 2^p < n - 1 <= 2^(p+1), starting with a(1) = a(2) = 1 and a(3) = 4.
%H A050036 Ivan Neretin, <a href="/A050036/b050036.txt">Table of n, a(n) for n = 1..8193</a>
%p A050036 a := proc(n) option remember;
%p A050036 `if`(n < 4, [1, 1, 4][n], a(n - 1) + a(-2^ceil(log[2](n - 1)) + 2*n - 3)):
%p A050036 end proc:
%p A050036 seq(a(n), n = 1..60); # _Petros Hadjicostas_, Nov 14 2019
%t A050036 Fold[Append[#1, #1[[-1]] + #1[[#2]]] &, {1, 1, 4}, Flatten@Table[2 k - 1, {n, 5}, {k, 2^n}]] (* _Ivan Neretin_, Sep 07 2015 *)
%Y A050036 Same as A050052 and A050068 except for second term.
%Y A050036 Cf. similar sequences with different initial conditions: A050024 (1,1,1), A050028 (1,1,2), A050032 (1,1,3), 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 A050036 nonn
%O A050036 1,3
%A A050036 _Clark Kimberling_
%E A050036 Name edited by _Petros Hadjicostas_, Nov 14 2019