cp's OEIS Frontend

A215289 Number of permutations of 0..floor((n*5-1)/2) on even squares of an n X 5 array such that each row and column of even squares is increasing.

%I A215289 #11 Aug 25 2025 10:11:54
%S A215289 1,10,140,2100,60060,1051050,42882840,814773960,41227562376,
%T A215289 824551247520,48236247979920,999179422441200,64899082486180800,
%U A215289 1379105502831342000,96951116849043342600,2100607531729272423000,157112712418611824074200,3456479673209460129632400,271742147399231010918736320
%N A215289 Number of permutations of 0..floor((n*5-1)/2) on even squares of an n X 5 array such that each row and column of even squares is increasing.
%H A215289 R. H. Hardin, <a href="/A215289/b215289.txt">Table of n, a(n) for n = 1..210</a>
%F A215289 a(n) = A060854(3,f3)*A060854(2,f4)*binomial(3*f3+2*f4,3*f3), where f3 = floor((n+1)/2) and f4 = floor(n/2).
%e A215289 Some solutions for n=5:
%e A215289 ..0..x..2..x..6....1..x..2..x..6....0..x..3..x..9....0..x..1..x..8
%e A215289 ..x..3..x..4..x....x..0..x..4..x....x..2..x..4..x....x..3..x..6..x
%e A215289 ..1..x..7..x.10....7..x..9..x.11....1..x..7..x.11....2..x..4..x..9
%e A215289 ..x..5..x.11..x....x..3..x..5..x....x..5..x..8..x....x..7..x.10..x
%e A215289 ..8..x..9..x.12....8..x.10..x.12....6..x.10..x.12....5..x.11..x.12
%Y A215289 Column 5 of A215292.
%K A215289 nonn,changed
%O A215289 1,2
%A A215289 _R. H. Hardin_, Aug 07 2012