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%I #8 Dec 14 2021 01:45:43
%S 1,1,1,1,5,8,19,22,69,121,341,406,1203,2155,6336,7624,22593,40717,
%T 121483,147001,438533,792351,2381512,2892044,8677763,15703156,
%U 47419503,57728737,173984792,315180458,954961034,1164727748,3522101709
%N a(n) = T(n, floor(n/2)), where T is given by A026584.
%H G. C. Greubel, <a href="/A026595/b026595.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) = A026584(n, floor(n/2))
%t T[n_, k_]:= T[n, k]= If[k==0 || k==2*n, 1, If[k==1 || k==2*n-1, Floor[n/2], If[EvenQ[n+k], T[n-1, k-2] + T[n-1, k], T[n-1, k-2] + T[n-1, k-1] + T[n-1, k] ]]]; (* T = A026584 *)
%t Table[T[n, Floor[n/2]], {n, 0, 40}] (* _G. C. Greubel_, Dec 13 2021 *)
%o (Sage)
%o @CachedFunction
%o def T(n, k): # T = A026584
%o if (k==0 or k==2*n): return 1
%o elif (k==1 or k==2*n-1): return (n//2)
%o else: return T(n-1, k-2) + T(n-1, k) if ((n+k)%2==0) else T(n-1, k-2) + T(n-1, k-1) + T(n-1, k)
%o [T(n, n//2) for n in (0..40)] # _G. C. Greubel_, Dec 13 2021
%Y Cf. A026584, A026585, A026587, A026589, A026590, A026591, A026592, A026593, A026594, A026596, A026597, A026598, A026599, A027282, A027283, A027284, A027285, A027286.
%K nonn
%O 0,5
%A _Clark Kimberling_
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