A049922 - OEIS

A049922

a(n) = a(1) + a(2) + ... + a(n-1) - a(m) for n >= 4, where m = n - 1 - 2^p and p is the unique integer such that 2^p < n - 1 <= 2^(p+1), starting with a(1) = 1, a(2) = 3 and a(3) = 2.

%I #18 May 06 2022 13:12:15

%S 1,3,2,5,8,18,34,69,135,274,546,1093,2183,4363,8716,17416,34797,69662,

%T 139322,278645,557287,1114571,2229132,4458248,8916461,17832856,

%U 35665573,71330874,142661201,285321312,570640444,1141276535,2282544370

%N a(n) = a(1) + a(2) + ... + a(n-1) - a(m) for n >= 4, where m = n - 1 - 2^p and p is the unique integer such that 2^p < n - 1 <= 2^(p+1), starting with a(1) = 1, a(2) = 3 and a(3) = 2.

%o (PARI) lista(nn) = { my(va = vector(nn)); va[1] = 1; va[2] = 3; va[3] = 2; my(sa = vecsum(va)); for (n=4, nn, va[n] = sa - va[n - 1 - 2^ceil(-1 + log(n-1)/log(2))]; sa += va[n]; ); va; } \\ _Petros Hadjicostas_, Apr 26 2020 (with nn > 2)

%Y Cf. A049923 (similar, but with minus a(2*m)), A049970 (similar, but with plus a(m)), A049971 (similar, but with plus a(2*m)).

%K nonn

%O 1,2

%A _Clark Kimberling_

%E Name edited by _Petros Hadjicostas_, Apr 26 2020