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A298412 a(n) = 2*a(n-1) + a(n-2) + a([n/2]), where a(0) = 1, a(1) = 1, a(2) = 1.

%I A298412 #5 Feb 11 2018 10:52:40
%S A298412 1,1,1,4,10,25,64,157,388,943,2299,5566,13495,32620,78892,190561,
%T A298412 460402,1111753,2684851,6482398,15651946,37788589,91234690,220263535,
%U A298412 531775255,1283827540,3099462955,7482786070,18065113987,43613092936,105291490420,254196264337
%N A298412 a(n) = 2*a(n-1) + a(n-2) + a([n/2]), where a(0) = 1, a(1) = 1, a(2) = 1.
%C A298412 a(n)/a(n-1) -> 1 + sqrt(2).
%H A298412 Clark Kimberling, <a href="/A298412/b298412.txt">Table of n, a(n) for n = 0..1000</a>
%t A298412 a[0] = 1; a[1] = 1; a[2] = 1;
%t A298412 a[n_] := a[n] = 2 a[n - 1] + a[n - 2] + a[Floor[n/2]];
%t A298412 Table[a[n], {n, 0, 30}]  (* A298412 *)
%Y A298412 Cf. A298338.
%K A298412 nonn,easy
%O A298412 0,4
%A A298412 _Clark Kimberling_, Feb 11 2018