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A151788 Partial sums of A151787.

%I A151788 #14 Oct 31 2022 13:00:48
%S A151788 1,4,7,13,16,22,28,40,43,49,55,67,73,85,97,121,124,130,136,148,154,
%T A151788 166,178,202,208,220,232,256,268,292,316,364,367,373,379,391,397,409,
%U A151788 421,445,451,463,475,499,511,535,559,607,613,625,637,661,673,697,721,769,781,805
%N A151788 Partial sums of A151787.
%H A151788 Robert Israel, <a href="/A151788/b151788.txt">Table of n, a(n) for n = 1..10000</a>
%H A151788 Hsien-Kuei Hwang, Svante Janson, and Tsung-Hsi Tsai, <a href="https://arxiv.org/abs/2210.10968">Identities and periodic oscillations of divide-and-conquer recurrences splitting at half</a>, arXiv:2210.10968 [cs.DS], 2022, p. 30.
%F A151788 G.f. g(x) satisfies g(x) = (2+1/x)*(1+x)*g(x^2) + x^2/(1-x). - _Robert Israel_, Feb 27 2018
%p A151788 wt:= n -> convert(convert(n,base,2),`+`):
%p A151788 ListTools:-PartialSums([1,seq(3*2^(wt(n-1)-1),n=2..100)]); # _Robert Israel_, Feb 27 2018
%t A151788 b[n_] := If[n == 1, 1, 3*2^(Total[IntegerDigits[n-1, 2]]-1)];
%t A151788 Array[b, 100] // Accumulate (* _Jean-François Alcover_, Mar 27 2019 *)
%o A151788 (PARI) b(n) = if (n==1, 1, 3*2^(hammingweight(n-1)-1));
%o A151788 a(n) = sum(k=1, n, b(k)); \\ _Michel Marcus_, Feb 27 2018
%Y A151788 Cf. A151787.
%K A151788 nonn
%O A151788 1,2
%A A151788 _N. J. A. Sloane_, Jun 25 2009