cp's OEIS Frontend

A027945 Greatest number in row n of array T given by A027935.

%I A027945 #10 Jun 06 2025 14:36:54
%S A027945 1,1,2,4,7,12,26,51,92,176,365,709,1300,2587,5270,10220,18955,38403,
%T A027945 77533,150438,281403,575333,1155661,2245004,4227273,8684673,17390359,
%U A027945 33828704,64250459,131901368,263589730,513445147,984880747,2013363836,4018052441,7836832057,15144704167,30860244790,61530661493
%N A027945 Greatest number in row n of array T given by A027935.
%H A027945 G. C. Greubel, <a href="/A027945/b027945.txt">Table of n, a(n) for n = 0..1000</a>
%t A027945 A027935[n_, k_]:= A027935[n,k]= Sum[Binomial[n-j, 2*(n-k-j)], {j,0,Floor[(2*n-2*k+ 1)/2]}];
%t A027945 b[n_]:= b[n]= Table[A027935[n,k], {k,0,n}]//Union;
%t A027945 A027945[n_]:= Max[b[n]];
%t A027945 Table[A027945[n], {n,0,50}] (* _G. C. Greubel_, Jun 06 2025 *)
%o A027945 (SageMath)
%o A027945 @CachedFunction
%o A027945 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 A027945 def b(n): return sorted(set(flatten([ A027935(n,k) for k in range(n+1)])))
%o A027945 def A027945(n): return max(b(n))
%o A027945 [A027945(n) for n in range(51)] # _G. C. Greubel_, Jun 06 2025
%Y A027945 Cf. A027935.
%K A027945 nonn
%O A027945 0,3
%A A027945 _Clark Kimberling_