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A026531 a(n) = T(n,0) + T(n,1) + ... + T(n,n), T given by A026519.

%I A026531 #11 Dec 21 2021 02:34:19
%S A026531 1,2,4,11,22,64,127,376,746,2222,4414,13180,26215,78373,156041,466840,
%T A026531 930194,2784266,5550976,16620976,33152042,99291358,198115526,
%U A026531 593484440,1184511095,3548969075,7084871668,21230215328,42390336619
%N A026531 a(n) = T(n,0) + T(n,1) + ... + T(n,n), T given by A026519.
%H A026531 G. C. Greubel, <a href="/A026531/b026531.txt">Table of n, a(n) for n = 0..1000</a>
%F A026531 a(n) = Sum_{j=0..n} A026519(n, j).
%t A026531 T[n_, k_]:= T[n, k]= If[k<0 || k>2*n, 0, If[k==0 || k==2*n, 1, If[k==1 || k==2*n-1, Floor[(n+1)/2], If[EvenQ[n], T[n-1, k-2] + T[n-1, k], T[n-1, k-1] + T[n - 1, k-2] + T[n-1, k] ]]]]; (* T = A026519 *)
%t A026531 a[n_]:= a[n]= Block[{$RecursionLimit = Infinity}, Sum[T[n, j], {j,0,n}] ];
%t A026531 Table[a[n], {n, 0, 40}] (* _G. C. Greubel_, Dec 20 2021 *)
%o A026531 (Sage)
%o A026531 @CachedFunction
%o A026531 def T(n,k): # T = A026519
%o A026531     if (k<0 or k>2*n): return 0
%o A026531     elif (k==0 or k==2*n): return 1
%o A026531     elif (k==1 or k==2*n-1): return (n+1)//2
%o A026531     elif (n%2==0): return T(n-1, k) + T(n-1, k-2)
%o A026531     else: return T(n-1, k) + T(n-1, k-1) + T(n-1, k-2)
%o A026531 @CachedFunction
%o A026531 def a(n): return sum( T(n,k) for k in (0..n) )
%o A026531 [a(n) for n in (0..40)] # _G. C. Greubel_, Dec 20 2021
%Y A026531 Cf. A026519, A026520, A026521, A026522, A026523, A026524, A026525, A026526, A026527, A026528, A026529, A026530, A026531, A026534, A027262, A027263, A027264, A027265, A027266.
%K A026531 nonn
%O A026531 0,2
%A A026531 _Clark Kimberling_