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A049885 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) = a(3) = 1.

%I A049885 #22 May 06 2022 13:12:15
%S A049885 1,1,1,2,4,7,15,30,60,91,197,402,807,1616,3233,6466,12932,19399,42031,
%T A049885 85679,172167,344739,689683,1379472,2758975,5517980,11035975,22071958,
%U A049885 44143919,88287840,176575681,353151362,706302724,1059454087
%N A049885 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) = a(3) = 1.
%F A049885 From _Petros Hadjicostas_, Nov 07 2019: (Start)
%F A049885 a(n) = -a(2^ceiling(log_2(n-1)) + 2 - n) + Sum_{i = 1..n-1} a(i) for n >= 4.
%F A049885 a(n) = -a(n - 1 - A006257(n-2)) + Sum_{i = 1..n-1} a(i) for n >= 4. (End)
%e A049885 From _Petros Hadjicostas_, Nov 07 2019: (Start)
%e A049885 a(4) = -a(2^ceiling(log_2(4-1)) + 2 - 4) + a(1) + a(2) + a(3) = -a(2) + a(1) + a(2) + a(3) = 2.
%e A049885 a(5) = -a(2^ceiling(log_2(5-1)) + 2 - 5) + a(1) + a(2) + a(3) + a(4) = -a(1) + a(1) + a(2) + a(3) + a(4) = 4.
%e A049885 a(6) = -a(2^ceiling(log_2(6-1)) + 2 - 6) + a(1) + a(2) + a(3) + a(4) + a(5) = -a(4) + a(1) + a(2) + a(3) + a(4) + a(5) = 7.
%e A049885 a(7) =  -a(7 - 1 - A006257(7-2)) + Sum_{i = 1..6} a(i) = -a(3) +  Sum_{i = 1..6} a(i) = 15.
%e A049885 a(8) =  -a(8 - 1 - A006257(8-2)) + Sum_{i = 1..7} a(i) = -a(2) +  Sum_{i = 1..7} a(i) = 30. (End)
%p A049885 s := proc(n) option remember; `if`(n < 1, 0, a(n) + s(n - 1)) end proc:
%p A049885 a := proc(n) option remember;
%p A049885 `if`(n < 4, 1, s(n - 1) - a(Bits:-Iff(n - 2, n - 2) + 3 - n)):
%p A049885 end proc:
%p A049885 seq(a(n), n = 1..34); # _Petros Hadjicostas_, Nov 07 2019
%o A049885 (PARI) lista(nn) = { my(va = vector(nn)); va[1] = 1; va[2] = 1; va[3] = 1; my(sa = vecsum(va)); for (n=4, nn, va[n] = sa - va[2 - n + 2^ceil(log(n-1)/log(2))]; sa += va[n]; ); va; } \\ _Petros Hadjicostas_, Apr 27 2020 (with nn > 2)
%Y A049885 Cf. A006257, A049933 (similar, but with plus a(m)).
%K A049885 nonn
%O A049885 1,4
%A A049885 _Clark Kimberling_
%E A049885 Name edited by _Petros Hadjicostas_, Nov 07 2019