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A063916 G.f.: (1 + Sum_{ i >= 0 } 2^i*x^(2^(i+1)-1)) / (1-x)^3.

%I A063916 #13 Nov 09 2020 09:15:13
%S A063916 1,4,9,18,31,48,69,98,135,180,233,294,363,440,525,626,743,876,1025,
%T A063916 1190,1371,1568,1781,2010,2255,2516,2793,3086,3395,3720,4061,4434,
%U A063916 4839,5276,5745,6246,6779,7344,7941,8570,9231,9924,10649,11406,12195,13016,13869
%N A063916 G.f.: (1 + Sum_{ i >= 0 } 2^i*x^(2^(i+1)-1)) / (1-x)^3.
%H A063916 Alois P. Heinz, <a href="/A063916/b063916.txt">Table of n, a(n) for n = 0..10000</a>
%p A063916 b:= proc(n) option remember; `if`(n<0, 0, 1+
%p A063916      (t-> 2*(b(floor(t))+b(ceil(t))))(n/2-1))
%p A063916     end:
%p A063916 a:= proc(n) option remember; `if`(n<0, 0, b(n)+a(n-1)) end:
%p A063916 seq(a(n), n=0..55);  # _Alois P. Heinz_, Jul 10 2019
%t A063916 b[n_] := b[n] = If[EvenQ[n], 2b[n/2] + 2b[n/2-1], 4b[(n-1)/2]]+1;
%t A063916 b[0] = 0; b[1] = 1; b[2] = 3;
%t A063916 b /@ Range[100] // Accumulate (* _Jean-François Alcover_, Nov 09 2020 *)
%Y A063916 Partial sums of A063915.
%K A063916 nonn
%O A063916 0,2
%A A063916 _N. J. A. Sloane_, Sep 01 2001
%E A063916 More terms from _Ralf Stephan_, Sep 15 2003