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A027977 a(n) = greatest number in row n of array T given by A027960.

%I A027977 #9 Jun 07 2025 16:42:35
%S A027977 1,3,4,8,15,28,54,101,199,373,743,1404,2801,5353,10636,20495,40615,
%T A027977 78753,155793,303553,599801,1173183,2316317,4544731,8968421,17641499,
%U A027977 34801731,68602923,135308317,267203186,526966454,1042217402,2055373383,4070330014,8027429651,15914813448,31389204737,62291326036,122871494899
%N A027977 a(n) = greatest number in row n of array T given by A027960.
%H A027977 G. C. Greubel, <a href="/A027977/b027977.txt">Table of n, a(n) for n = 0..1000</a>
%t A027977 T[n_, k_]:= T[n, k]= If[k<0 || k>2*n, 0, If[k==0 || k==2*n, 1, If[k==1, 3, T[n-1, k-2] + T[n-1, k-1]]]]; (* T = A027960 *)
%t A027977 b[n_]:= b[n]= Table[T[n,k], {k,0,2*n}]//Union;
%t A027977 A027977[n_]:= Max[b[n]];
%t A027977 Table[A027977[n], {n,0,50}] (* _G. C. Greubel_, Jun 07 2025 *)
%o A027977 (SageMath)
%o A027977 @CachedFunction
%o A027977 def T(n, k): # T = A027960
%o A027977     if (k<0 or k>2*n): return 0
%o A027977     elif (k==0 or k==2*n): return 1
%o A027977     elif (k==1): return 3
%o A027977     else: return T(n-1, k-2) + T(n-1, k-1)
%o A027977 def b(n): return sorted(set(flatten([T(n,k) for k in range(2*n+1)])))
%o A027977 def A027977(n): return max(b(n))
%o A027977 print([A027977(n) for n in range(51)]) # _G. C. Greubel_, Jun 07 2025
%Y A027977 Cf. A027960.
%K A027977 nonn
%O A027977 0,2
%A A027977 _Clark Kimberling_
%E A027977 More terms added by _G. C. Greubel_, Jun 07 2025