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A026645 a(n) = Sum_{k=0..floor(n/2)} A026637(n, k).

%I A026645 #11 Jun 30 2024 03:11:34
%S A026645 1,1,3,5,14,21,55,85,216,341,848,1365,3340,5461,13191,21845,52208,
%T A026645 87381,206968,349525,821514,1398101,3264044,5592405,12979006,22369621,
%U A026645 51642594,89478485,205592744,357913941,818848135,1431655765,3262611696,5726623061,13003800704,22906492245
%N A026645 a(n) = Sum_{k=0..floor(n/2)} A026637(n, k).
%H A026645 G. C. Greubel, <a href="/A026645/b026645.txt">Table of n, a(n) for n = 0..1000</a>
%t A026645 T[n_, k_]:= T[n, k]= If[k==0 || k==n, 1, If[k==1 || k==n-1, Floor[(3*n- 1)/2], T[n-1,k] + T[n-1,k-1] ]];
%t A026645 A026645[n_]:= Sum[T[n, k], {k, 0, Floor[n/2]}];
%t A026645 Table[A026645[n], {n,0,40}] (* _G. C. Greubel_, Jun 29 2024 *)
%o A026645 (SageMath)
%o A026645 @CachedFunction
%o A026645 def T(n,k): # T = A026637
%o A026645     if k==0 or k==n: return 1
%o A026645     elif k==1 or k==n-1: return ((3*n-1)//2)
%o A026645     else: return T(n-1, k) + T(n-1, k-1)
%o A026645 def A026645(n): return sum(T(n,k) for k in range((n//2)+1))
%o A026645 [A026645(n) for n in range(41)] # _G. C. Greubel_, Jun 29 2024
%Y A026645 Cf. A026637, A026638, A026639, A026640, A026642, A026643, A026644.
%Y A026645 Cf. A026646, A026647, A026966, A026967, A026968, A026969, A026970.
%K A026645 nonn
%O A026645 0,3
%A A026645 _Clark Kimberling_