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

1, 1, 2, 3, 7, 14, 25, 46, 97, 189, 344, 674, 1383, 2683, 4950, 9955, 20175, 39130, 72905, 148487, 298925, 580328, 1089343, 2233409, 4478413, 8705686, 16438345, 33822205, 67650909, 131688362, 251448212, 515037942, 1028483089, 2004688605, 3860656125, 7878708566, 15715540623, 30670416703, 59451560083

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A027948.

Programs

Magma

A027948:= func< n,k | k eq n select 1 else (&+[Binomial(n-j, 2*(n-k-j)-1): j in [0..n-k]]) >;
b:= func< n | [A027948(n,k): k in [0..n]] >;
A027957:= func< n | Max( b(n) ) >;
[A027957(n): n in [0..50]]; // G. C. Greubel, Jun 08 2025

Mathematica

A027948[n_, k_]:= A027948[n, k]= If[k==n, 1, Sum[Binomial[n-j, 2*(n-k-j)-1], {j,0,n- k}]];
b[n_]:= b[n]= Table[A027948[n,k], {k,0,n}]//Union;
A027957[n_]:= Max[b[n]];
Table[A027957[n], {n,0,50}] (* G. C. Greubel, Jun 07 2025 *)

SageMath

@CachedFunction
def A027948(n, k):
    if (k==n): return 1
    else: return sum(binomial(n-j, 2*(n-k-j)-1) for j in (0..n-k))
def b(n): return sorted(set(flatten([ A027948(n,k) for k in range(n+1)])))
def A027957(n): return max(b(n))
print([A027957(n) for n in range(51)]) # G. C. Greubel, Jun 07 2025

Extensions

More terms added by G. C. Greubel, Jun 07 2025