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%I #12 Oct 13 2022 04:54:43
%S 1,2,4,4,8,12,24,40,80,140,280,504,1008,1848,3696,6864,13728,25740,
%T 51480,97240,194480,369512,739024,1410864,2821728,5408312,10816624,
%U 20801200,41602400,80233200,160466400,310235040,620470080,1202160780
%N a(n) = Sum_{j=0..n} A047072(j, n-j).
%H G. C. Greubel, <a href="/A047073/b047073.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) = 2*A063886(n-1) + (n+1)*[n<2].
%F G.f.: 1 + 2*x*sqrt((1+2*x)/(1-2*x)). - _Michael Somos_
%t Table[If[n<2, n+1, 4*Binomial[n-2, Floor[(n-2)/2]]], {n,0,40}] (* _G. C. Greubel_, Oct 13 2022 *)
%o (PARI) a(n) = if(n<2, max(0,n+1), 4*binomial(n-2, n\2-1))
%o (Magma) [n le 1 select n+1 else 4*Binomial(n-2, Floor((n-2)/2)): n in [0..40]]; // _G. C. Greubel_, Oct 13 2022
%o (SageMath) [4*binomial(n-2, ((n-2)//2)) + (n+1)*int(n<2) for n in range(41)] # _G. C. Greubel_, Oct 13 2022
%Y Cf. A047072, A063886.
%K nonn
%O 0,2
%A _Clark Kimberling_
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