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A027936 Uniquification of array T given by A027935.

%I A027936 #8 Jun 06 2025 03:30:26
%S A027936 1,2,4,5,7,11,12,13,16,22,26,29,33,34,37,46,51,56,67,79,88,89,92,106,
%T A027936 121,137,154,155,172,176,191,211,221,232,233,247,254,277,301,326,352,
%U A027936 365,376,379,407,436,466,497,529,530,551,562,596
%N A027936 Uniquification of array T given by A027935.
%H A027936 G. C. Greubel, <a href="/A027936/b027936.txt">Table of n, a(n) for n = 1..5000</a>
%t A027936 A027935[n_, k_]:= A027935[n, k]= Sum[Binomial[n-j, 2*(n-k-j)], {j,0,Floor[(2*n-2*k+ 1)/2]}];
%t A027936 A027936= Table[A027935[n,k], {n,0,225}, {k,0,n}]//Flatten//Union;
%t A027936 Table[A027936[[n]], {n,100}] (* _G. C. Greubel_, Jun 06 2025 *)
%o A027936 (SageMath)
%o A027936 @CachedFunction
%o A027936 def A027935(n,k): return sum(binomial(n-j, 2*(n-k-j)) for j in range(int((2*n-2*k+1)/2+1)) )
%o A027936 A027936 = sorted(set(flatten([[ A027935(n,k) for k in range(n+1)] for n in range(103)])))
%o A027936 print([A027936[n] for n in range(100)]) # _G. C. Greubel_, Jun 06 2025
%Y A027936 Cf. A027935.
%K A027936 nonn
%O A027936 1,2
%A A027936 _Clark Kimberling_