A349862 - OEIS

%I #25 Jan 05 2022 05:33:29

%S 1,1,1,1,2,3,4,5,6,10,15,21,28,36,56,84,120,165,220,330,495,715,1001,

%T 1365,2002,3003,4368,6188,8568,12376,18564,27132,38760,54264,77520,

%U 116280,170544,245157,346104,490314,735471,1081575,1562275,2220075,3124550,4686825,6906900,10015005,14307150

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

%e a(7) = 5 since row n=7 of A102547 is 1, 5, 3 and the maximum value is 5.

%e 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.

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

%o (PARI) a(n) = vecmax(vector(n\3+1, k, k--; binomial(n-2*k, k))); \\ _Michel Marcus_, Dec 06 2021

%o (Python)

%o from math import comb

%o def A349862(n): return max(comb(n-2*k,k) for k in range(n//3+1)) # _Chai Wah Wu_, Jan 04 2022

%Y Maximum row values of A102547.

%Y Cf. A073028.

%K nonn

%O 0,5

%A _Enrique Navarrete_, Dec 02 2021