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A298415 a(n) = a(n-1) + 2*a(n-2) + a([n/2]), where a(0) = 1, a(1) = 1, a(2) = 1.

%I A298415 #4 Feb 11 2018 10:52:25
%S A298415 1,1,1,4,7,16,34,70,145,292,598,1198,2428,4858,9784,19570,39283,78568,
%T A298415 157426,314854,630304,1260610,2522416,5044834,10092094,20184190,
%U A298415 40373236,80746474,161502730,323005462,646030492,1292060986,2584161253,5168322508,10336723582
%N A298415 a(n) = a(n-1) + 2*a(n-2) + a([n/2]), where a(0) = 1, a(1) = 1, a(2) = 1.
%H A298415 Clark Kimberling, <a href="/A298415/b298415.txt">Table of n, a(n) for n = 0..1000</a>
%t A298415 a[0] = 1; a[1] = 1; a[2] = 1;
%t A298415 a[n_] := a[n] = a[n - 1] + 2 a[n - 2] + a[Floor[n/2]];
%t A298415 Table[a[n], {n, 0, 30}]  (* A298415 *)
%Y A298415 Cf. A298338.
%K A298415 nonn,easy
%O A298415 0,4
%A A298415 _Clark Kimberling_, Feb 11 2018