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A224257 Number of n X 3 0..2 arrays with rows, diagonals and antidiagonals unimodal and columns nondecreasing.

%I A224257 #11 Mar 18 2025 22:33:10
%S A224257 22,158,648,2017,5246,11990,24842,47643,85838,146878,240668,380061,
%T A224257 581398,865094,1256270,1785431,2489190,3411038,4602160,6122297,
%U A224257 8040654,10436854,13401938,17039411,21466334,26814462,33231428,40881973,49949222,60636006,73166230,87786287
%N A224257 Number of n X 3 0..2 arrays with rows, diagonals and antidiagonals unimodal and columns nondecreasing.
%H A224257 R. H. Hardin, <a href="/A224257/b224257.txt">Table of n, a(n) for n = 1..210</a>
%F A224257 Empirical: a(n) = (23/360)*n^6 + (19/40)*n^5 + (211/72)*n^4 + (119/24)*n^3 + (2161/180)*n^2 + (77/30)*n - 1.
%F A224257 Conjectures from _Colin Barker_, Aug 29 2018: (Start)
%F A224257 G.f.: x*(22 + 4*x + 4*x^2 + 29*x^3 - 25*x^4 + 13*x^5 - x^6) / (1 - x)^7.
%F A224257 a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.
%F A224257 (End)
%e A224257 Some solutions for n=3:
%e A224257 ..0..1..0....0..0..1....0..1..1....2..2..0....0..0..0....1..2..0....0..0..0
%e A224257 ..2..1..0....0..1..1....2..2..2....2..2..0....2..1..1....2..2..1....0..0..0
%e A224257 ..2..1..1....1..1..2....2..2..2....2..2..2....2..2..1....2..2..2....2..2..0
%Y A224257 Column 3 of A224262.
%K A224257 nonn
%O A224257 1,1
%A A224257 _R. H. Hardin_, Apr 02 2013
%E A224257 Name corrected by _Andrew Howroyd_, Mar 18 2025