A094291 a(n) = maximal value of C(i, j) * C(n-j, n-i) for 0 <= j <= i <= n.

1, 2, 4, 9, 18, 40, 100, 225, 525, 1225, 3136, 7056, 17640, 44100, 108900, 261360, 637065, 1656369, 4008004, 10020010, 25050025, 64128064, 155739584, 393853824, 1012766976, 2538950544, 6347376360, 15868440900, 41408180100, 102252852900

Offset: 1

Author

Hugo van der Sanden, Jun 15 2004

Keywords

• nonn

Comments

This is the number of longest common subsequences between two binary strings of the form 00...011...1.

This is a lower bound for A094837, equivalent to choosing first string (x "a"s followed by (n-x) "b"s) and second string (y "a"s followed by (n-y) "b"s).

Examples

			a(3) is maximal with x=1, y=2, giving a(3) = C(2,1) * C(3-1,3-2). This is equivalent to the number of instances of length-2 common subsequences between "aab" and "abb".
		

Crossrefs

Cf. A094858-A094862, A094837, A094824, A094349, A094350.