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A224265 Number of 5 X n 0..2 arrays with rows, diagonals and antidiagonals unimodal and columns nondecreasing.

%I A224265 #7 Mar 18 2025 22:32:32
%S A224265 21,441,5246,41012,238366,1122522,4542734,16423026,54399996,167906334,
%T A224265 488545330,1351296894,3575548984,9095336020,22330458551,53087335395,
%U A224265 122539314344,275260139864,602890604743,1289688693983,2698414556120,5529127445368,11107359382330
%N A224265 Number of 5 X n 0..2 arrays with rows, diagonals and antidiagonals unimodal and columns nondecreasing.
%H A224265 R. H. Hardin, <a href="/A224265/b224265.txt">Table of n, a(n) for n = 1..210</a>
%F A224265 Empirical: a(n) = (1/1379196149760000)*n^20 - (1/137919614976000)*n^19 + (293/304874938368000)*n^18 + (1/4619317248000)*n^17 + (157/352235520000)*n^16 + (8317/2092278988800)*n^15 + (2780521/20922789888000)*n^14 + (383809/213497856000)*n^13 + (203282759/6897623040000)*n^12 + (34268483/229920768000)*n^11 + (1734251209/357654528000)*n^10 + (5309275061/1609445376000)*n^9 + (4327647950569/17435658240000)*n^8 + (321770123/1257984000)*n^7 + (506327783081/101896704000)*n^6 - (990071393771/62270208000)*n^5 + (554590430608603/18525386880000)*n^4 - (8854141496479/77189112000)*n^3 + (188734999923373/97772875200)*n^2 - (257473009033/29099070)*n + 13615 for n>4.
%e A224265 Some solutions for n=3:
%e A224265 ..0..0..0....0..0..1....0..1..2....0..0..0....0..1..0....1..0..0....0..1..0
%e A224265 ..0..0..0....0..1..1....0..1..2....0..0..0....0..1..0....1..1..0....0..1..0
%e A224265 ..0..1..2....0..1..1....0..1..2....0..0..1....0..1..0....1..1..0....1..1..1
%e A224265 ..0..2..2....0..2..1....1..1..2....1..1..1....0..1..0....1..2..0....1..2..1
%e A224265 ..2..2..2....2..2..1....1..1..2....1..2..2....1..1..2....2..2..1....2..2..1
%Y A224265 Row 5 of A224262.
%K A224265 nonn
%O A224265 1,1
%A A224265 _R. H. Hardin_, Apr 02 2013
%E A224265 Name corrected by _Andrew Howroyd_, Mar 18 2025