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A223923 Number of 6Xn 0..2 arrays with rows and antidiagonals unimodal and columns nondecreasing.

%I A223923 #6 Jul 23 2025 04:39:25
%S A223923 28,784,12752,139925,1147712,7526024,41334135,196691651,831996762,
%T A223923 3191126598,11273703656,37147879480,115325935123,340079259419,
%U A223923 958837466287,2598467396144,6797368250655,17222433541791,42380526618210
%N A223923 Number of 6Xn 0..2 arrays with rows and antidiagonals unimodal and columns nondecreasing.
%C A223923 Row 6 of A223918
%H A223923 R. H. Hardin, <a href="/A223923/b223923.txt">Table of n, a(n) for n = 1..210</a>
%F A223923 Empirical: a(n) = (1/35608838483312640000)*n^24 + (1/593480641388544000)*n^23 + (1/11491439984640000)*n^22 + (2153/709596419051520000)*n^21 + (219067/2432902008176640000)*n^20 + (25141/11058645491712000)*n^19 + (7669183/149388719800320000)*n^18 + (2894807/2766457774080000)*n^17 + (345585431/17575143505920000)*n^16 + (19926331/58583811686400)*n^15 + (19845690451/3766102179840000)*n^14 + (29105209667/470762772480000)*n^13 + (9676615094071/17575143505920000)*n^12 + (3447815819587/878757175296000)*n^11 + (1672600520777/75107450880000)*n^10 + (40399178860907/399435079680000)*n^9 + (5902479263543591/16005934264320000)*n^8 + (857508181884829/800296713216000)*n^7 + (1309477651758586831/532197314288640000)*n^6 + (43433412218488139/9855505820160000)*n^5 + (4693314253940149/778066248960000)*n^4 + (1959925243391/320817246750)*n^3 + (12456072565753/2698531355520)*n^2 + (3225389971/1784742960)*n + 1
%e A223923 Some solutions for n=3
%e A223923 ..0..0..0....0..0..0....0..2..1....0..1..1....0..0..0....0..1..0....0..2..0
%e A223923 ..0..1..0....2..1..0....1..2..1....0..1..1....0..1..0....0..1..0....0..2..0
%e A223923 ..0..1..2....2..1..0....1..2..1....0..1..1....0..1..0....0..2..2....0..2..0
%e A223923 ..0..1..2....2..1..0....1..2..2....0..1..2....0..1..0....0..2..2....0..2..0
%e A223923 ..0..2..2....2..1..0....2..2..2....0..1..2....1..1..0....1..2..2....0..2..0
%e A223923 ..1..2..2....2..1..0....2..2..2....0..2..2....1..2..1....1..2..2....1..2..2
%K A223923 nonn
%O A223923 1,1
%A A223923 _R. H. Hardin_ Mar 29 2013