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

1, 3, 4, 8, 15, 28, 54, 101, 199, 373, 743, 1404, 2801, 5353, 10636, 20495, 40615, 78753, 155793, 303553, 599801, 1173183, 2316317, 4544731, 8968421, 17641499, 34801731, 68602923, 135308317, 267203186, 526966454, 1042217402, 2055373383, 4070330014, 8027429651, 15914813448, 31389204737, 62291326036, 122871494899

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

Links

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

Crossrefs

Cf. A027960.

Programs

Mathematica

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 *)
b[n_]:= b[n]= Table[T[n,k], {k,0,2*n}]//Union;
A027977[n_]:= Max[b[n]];
Table[A027977[n], {n,0,50}] (* G. C. Greubel, Jun 07 2025 *)

SageMath

@CachedFunction
def T(n, k): # T = A027960
    if (k<0 or k>2*n): return 0
    elif (k==0 or k==2*n): return 1
    elif (k==1): return 3
    else: return T(n-1, k-2) + T(n-1, k-1)
def b(n): return sorted(set(flatten([T(n,k) for k in range(2*n+1)])))
def A027977(n): return max(b(n))
print([A027977(n) for n in range(51)]) # G. C. Greubel, Jun 07 2025

Extensions

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