cp's OEIS Frontend

A027957 a(n) = greatest number in row n of array T given by A027948.

%I A027957 #12 Jun 09 2025 10:25:58
%S A027957 1,1,2,3,7,14,25,46,97,189,344,674,1383,2683,4950,9955,20175,39130,
%T A027957 72905,148487,298925,580328,1089343,2233409,4478413,8705686,16438345,
%U A027957 33822205,67650909,131688362,251448212,515037942,1028483089,2004688605,3860656125,7878708566,15715540623,30670416703,59451560083
%N A027957 a(n) = greatest number in row n of array T given by A027948.
%H A027957 G. C. Greubel, <a href="/A027957/b027957.txt">Table of n, a(n) for n = 0..1000</a>
%t A027957 A027948[n_, k_]:= A027948[n, k]= If[k==n, 1, Sum[Binomial[n-j, 2*(n-k-j)-1], {j,0,n- k}]];
%t A027957 b[n_]:= b[n]= Table[A027948[n,k], {k,0,n}]//Union;
%t A027957 A027957[n_]:= Max[b[n]];
%t A027957 Table[A027957[n], {n,0,50}] (* _G. C. Greubel_, Jun 07 2025 *)
%o A027957 (SageMath)
%o A027957 @CachedFunction
%o A027957 def A027948(n, k):
%o A027957     if (k==n): return 1
%o A027957     else: return sum(binomial(n-j, 2*(n-k-j)-1) for j in (0..n-k))
%o A027957 def b(n): return sorted(set(flatten([ A027948(n,k) for k in range(n+1)])))
%o A027957 def A027957(n): return max(b(n))
%o A027957 print([A027957(n) for n in range(51)]) # _G. C. Greubel_, Jun 07 2025
%o A027957 (Magma)
%o A027957 A027948:= func< n,k | k eq n select 1 else (&+[Binomial(n-j, 2*(n-k-j)-1): j in [0..n-k]]) >;
%o A027957 b:= func< n | [A027948(n,k): k in [0..n]] >;
%o A027957 A027957:= func< n | Max( b(n) ) >;
%o A027957 [A027957(n): n in [0..50]]; // _G. C. Greubel_, Jun 08 2025
%Y A027957 Cf. A027948.
%K A027957 nonn
%O A027957 0,3
%A A027957 _Clark Kimberling_
%E A027957 More terms added by _G. C. Greubel_, Jun 07 2025