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

1, 1, 2, 4, 7, 12, 26, 51, 92, 176, 365, 709, 1300, 2587, 5270, 10220, 18955, 38403, 77533, 150438, 281403, 575333, 1155661, 2245004, 4227273, 8684673, 17390359, 33828704, 64250459, 131901368, 263589730, 513445147, 984880747, 2013363836, 4018052441, 7836832057, 15144704167, 30860244790, 61530661493

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

Links

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

Crossrefs

Cf. A027935.

Programs

Mathematica

A027935[n_, k_]:= A027935[n,k]= Sum[Binomial[n-j, 2*(n-k-j)], {j,0,Floor[(2*n-2*k+ 1)/2]}];
b[n_]:= b[n]= Table[A027935[n,k], {k,0,n}]//Union;
A027945[n_]:= Max[b[n]];
Table[A027945[n], {n,0,50}] (* G. C. Greubel, Jun 06 2025 *)

SageMath

@CachedFunction
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)) )
def b(n): return sorted(set(flatten([ A027935(n,k) for k in range(n+1)])))
def A027945(n): return max(b(n))
[A027945(n) for n in range(51)] # G. C. Greubel, Jun 06 2025