%I #20 May 06 2022 13:12:15
%S 1,1,3,4,5,13,23,37,50,136,269,529,1034,1969,3545,5650,7619,20887,
%T 41771,83533,167042,333985,667577,1333714,2663747,5312257,10561868,
%U 20873284,40746839,77515135,139469243,222296635,299811770,821920174
%N a(n) = a(1) + a(2) + ... + a(n-1) - a(m) for n >= 4, where m = 2*n - 2 - 2^(p+1) 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.
%p s := proc(n) option remember; `if`(n < 1, 0, a(n) + s(n - 1)) end proc:
%p a := proc(n) option remember; `if`(n < 4, [1, 1, 3][n],
%p s(n - 1) - a(-2^ceil(log[2](n - 1)) + 2*n - 2))
%p end proc:
%p seq(a(n), n = 1..40); # _Petros Hadjicostas_, Nov 19 2019
%Y Cf. A049894 (similar, but with minus a(m/2)), A049942 (similar, but with plus a(m/2)), A049943 (similar, but with plus a(m)).
%K nonn
%O 1,3
%A _Clark Kimberling_
%E Name edited by _Petros Hadjicostas_, Nov 19 2019