A349862 a(n) is the maximum value of binomial(n-2*k,k) with 0 <= k <= floor(n/3).

1, 1, 1, 1, 2, 3, 4, 5, 6, 10, 15, 21, 28, 36, 56, 84, 120, 165, 220, 330, 495, 715, 1001, 1365, 2002, 3003, 4368, 6188, 8568, 12376, 18564, 27132, 38760, 54264, 77520, 116280, 170544, 245157, 346104, 490314, 735471, 1081575, 1562275, 2220075, 3124550, 4686825, 6906900, 10015005, 14307150

Offset: 0

Author

Enrique Navarrete, Dec 02 2021

Keywords

• nonn

Examples

			a(7) = 5 since row n=7 of A102547 is 1, 5, 3 and the maximum value is 5.
a(20) = 495 since row n=20 of A102547 is 1, 18, 120, 364, 495, 252, 28. The maximum value of 495 occurs at k = 4.
		

Crossrefs

Maximum row values of A102547.

Cf. A073028.

Programs

Mathematica

a[n_]:=Max[Table[Binomial[n-2k,k],{k,0,Floor[n/3]}]]; Array[a,49,0] (* Stefano Spezia, Dec 06 2021 *)

PARI

a(n) = vecmax(vector(n\3+1, k, k--; binomial(n-2*k, k))); \\ Michel Marcus, Dec 06 2021

Python

from math import comb
def A349862(n): return max(comb(n-2*k,k) for k in range(n//3+1)) # Chai Wah Wu, Jan 04 2022