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A224206 Number of 4Xn 0..3 arrays with rows unimodal and antidiagonals nondecreasing.

%I A224206 #6 Jul 23 2025 05:03:24
%S A224206 256,16000,263516,2411246,16355242,93052770,475218035,2252100875,
%T A224206 10026501335,42033573628,165872759545,616278459399,2159074455116,
%U A224206 7151151269790,22464417502819,67161353094487,191751351630146
%N A224206 Number of 4Xn 0..3 arrays with rows unimodal and antidiagonals nondecreasing.
%C A224206 Row 4 of A224204
%H A224206 R. H. Hardin, <a href="/A224206/b224206.txt">Table of n, a(n) for n = 1..210</a>
%F A224206 Empirical: a(n) = (1/2906843957821440000)*n^24 + (11/242236996485120000)*n^23 + (4897/1529252690853888000)*n^22 + (2857/19308746096640000)*n^21 + (973909/198604245565440000)*n^20 + (93229/757205729280000)*n^19 + (266789/109442285568000)*n^18 + (104478641/2667655710720000)*n^17 + (1429093157/2738983403520000)*n^16 + (4913895191/836911595520000)*n^15 + (171672001139/3012881743872000)*n^14 + (29350223359/59779399680000)*n^13 + (433008014137969/110472330608640000)*n^12 + (76105242218503/2510734786560000)*n^11 + (344040677347481/1506440871936000)*n^10 + (4054053159749/2583060480000)*n^9 + (276889384664596819/32011868528640000)*n^8 + (4163175202299941/127031224320000)*n^7 + (2967972507533347/42533251891200)*n^6 + (338490515487987437/4223788208640000)*n^5 + (85995749191634941/527973526080000)*n^4 - (9502462212673/345080736000)*n^3 - (23527482078379273/74209612276800)*n^2 + (572648006969/535422888)*n - 1055 for n>2
%e A224206 Some solutions for n=3
%e A224206 ..1..0..0....0..2..2....0..0..2....0..0..0....2..2..2....2..2..0....0..2..1
%e A224206 ..3..2..1....3..2..1....3..2..0....3..2..1....2..2..0....3..0..0....3..3..0
%e A224206 ..2..2..3....2..1..1....3..1..1....3..2..1....2..2..2....3..2..0....3..2..0
%e A224206 ..3..3..3....1..2..3....3..3..3....2..2..3....2..2..2....2..2..3....2..2..1
%K A224206 nonn
%O A224206 1,1
%A A224206 _R. H. Hardin_ Apr 01 2013