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A049893 a(n) = a(1) + a(2) + ... + a(n-1) - a(m) for n >= 4, 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) = a(2) = 1 and a(3) = 3.

%I A049893 #19 Oct 21 2024 13:14:58
%S A049893 1,1,3,4,8,13,27,56,112,169,367,748,1501,3006,6013,12028,24056,36085,
%T A049893 78185,159377,320259,641271,1282923,2566044,5132145,10264346,20528721,
%U A049893 41057456,82114917,164229838,328459677,656919356,1313838712,1970758069,4269975817,8704181473
%N A049893 a(n) = a(1) + a(2) + ... + a(n-1) - a(m) for n >= 4, 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) = a(2) = 1 and a(3) = 3.
%H A049893 Michael De Vlieger, <a href="/A049893/b049893.txt">Table of n, a(n) for n = 1..3326</a>
%H A049893 Frankie Mennicucci, <a href="https://digitalcommons.montclair.edu/etd/1406/">On the Number of Strong Dominating Sets in a Graph</a>, Master's Thesis, Montclair State Univ. (2024). See p. 17.
%p A049893 s := proc(n) option remember; `if`(n < 1, 0, a(n) + s(n - 1)) end proc:
%p A049893 a := proc(n) option remember;
%p A049893 `if`(n < 4, [1,1,3][n], s(n - 1) - a(2^ceil(log[2](n - 1)) + 2 - n)):
%p A049893 end proc:
%p A049893 seq(a(n), n = 1..34); # _Petros Hadjicostas_, Nov 11 2019
%t A049893 nn = 36; a[1] = a[2] = 1; a[3] = 3; s = 5; Do[Set[k, s - a[2^(Ceiling@ Log2[n - 1]) + 2 - n]]; a[n] = k; s += k, {n, 4, nn}]; Array[a, nn] (* _Michael De Vlieger_, Oct 21 2024 *)
%Y A049893 Cf. A049885.
%K A049893 nonn
%O A049893 1,3
%A A049893 _Clark Kimberling_
%E A049893 Name edited by _Petros Hadjicostas_, Nov 11 2019
%E A049893 More terms from _Michael De Vlieger_, Oct 21 2024