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%I #18 Nov 14 2019 10:43:43
%S 1,3,4,7,8,15,19,22,23,45,64,79,87,94,98,101,102,203,301,395,482,561,
%T 625,670,693,715,734,749,757,764,768,771,772,1543,2311,3075,3832,4581,
%U 5315,6030,6723,7393,8018,8579,9061,9456,9757
%N a(n) = a(n-1) + a(m) for n >= 3, where m = 2^(p+1) + 2 - n and p is the unique integer such that 2^p < n - 1 <= 2^(p+1), starting with a(1) = 1 and a(2) = 3.
%C In the Mathematica program below, the author of the program uses a(1) = 1, a(2) = 3, and a(3) = 4 as initial conditions. This is not necessary. We get the same sequence using only a(1) = 1 and a(2) = 3 as initial conditions. - _Petros Hadjicostas_, Nov 13 2019
%H Ivan Neretin, <a href="/A050069/b050069.txt">Table of n, a(n) for n = 1..8193</a>
%p a := proc(n) option remember;
%p `if`(n < 3, [1, 3][n], a(n - 1) + a(Bits:-Iff(n - 2, n - 2) + 3 - n)); end proc;
%p seq(a(n), n = 1 .. 48); # _Petros Hadjicostas_, Nov 08 2019
%t Fold[Append[#1, #1[[-1]] + #1[[#2]]] &, {1, 3, 4}, Flatten@Table[k, {n, 5}, {k, 2^n, 1, -1}]] (* _Ivan Neretin_, Sep 08 2015 *)
%Y Cf. similar sequences with different initial conditions: A050025 (1,1,1), A050029 (1,1,2), A050033 (1,1,3), A050037 (1,1,4), A050041 (1,2,1), A050045 (1,2,2), A050049 (1,2,3), A050053 (1,2,4), A050057 (1,3,1), A050061 (1,3,2), A050065 (1,3,3).
%K nonn
%O 1,2
%A _Clark Kimberling_
%E Name edited by _Petros Hadjicostas_, Nov 08 2019
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