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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) = a(2) = 1 and a(3) = 3.
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%I #13 May 06 2022 13:12:15

%S 1,1,3,4,8,16,32,62,123,249,498,994,1987,3970,7932,15848,31666,63393,

%T 126786,253570,507139,1014274,2028540,4057064,8114098,16228135,

%U 32456144,64912039,129823582,259646171,519290359,1038576756,2077145596

%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) = a(2) = 1 and a(3) = 3.

%o (PARI) lista(nn) = { nn = max(nn, 3); my(va = vector(nn)); va[1] = 1; va[2] = 1; va[3] = 3; my(sa = vecsum(va)); for (n=4, nn, va[n] = sa - va[n - 1 - 2^logint(n-2, 2)]; sa += va[n]; ); va; } \\ _Petros Hadjicostas_, May 03 2020

%Y Cf. A049895 (similar, but with minus a(2*m)), A049942 (similar, but with plus a(m)), A049943 (similar, but with plus a(2*m)).

%K nonn

%O 1,3

%A _Clark Kimberling_

%E Name edited by _Petros Hadjicostas_, May 03 2020