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A224258 Number of n X 4 0..2 arrays with rows, diagonals and antidiagonals unimodal and columns nondecreasing.

%I A224258 #11 Mar 18 2025 22:33:05
%S A224258 46,548,3096,12467,41012,116692,296646,688533,1482310,2995516,5735542,
%T A224258 10482777,18398930,31165238,51155680,81650727,127097568,193423162,
%U A224258 288406876,422119879,607438872,860642144,1202096354,1657042849,2256492738,3038240352,4048005130,5340712381
%N A224258 Number of n X 4 0..2 arrays with rows, diagonals and antidiagonals unimodal and columns nondecreasing.
%H A224258 R. H. Hardin, <a href="/A224258/b224258.txt">Table of n, a(n) for n = 1..210</a>
%F A224258 Empirical: a(n) = (41/4032)*n^8 + (9/112)*n^7 + (349/480)*n^6 + (69/20)*n^5 + (1325/192)*n^4 + (1571/48)*n^3 + (87503/5040)*n^2 - (21949/420)*n + 43 for n>2.
%F A224258 Conjectures from _Colin Barker_, Aug 29 2018: (Start)
%F A224258 G.f.: x*(46 + 134*x - 180*x^2 + 467*x^3 + 29*x^4 - 416*x^5 + 534*x^6 - 255*x^7 + 61*x^8 - 12*x^9 + 2*x^10) / (1 - x)^9.
%F A224258 a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>11.
%F A224258 (End)
%e A224258 Some solutions for n=3:
%e A224258 ..0..0..2..0....0..0..1..2....0..0..0..0....0..0..0..0....0..1..1..0
%e A224258 ..0..0..2..0....0..0..1..2....1..1..2..1....0..1..1..0....0..2..2..1
%e A224258 ..0..2..2..1....0..0..2..2....1..2..2..2....1..2..2..2....1..2..2..2
%Y A224258 Column 4 of A224262.
%K A224258 nonn
%O A224258 1,1
%A A224258 _R. H. Hardin_, Apr 02 2013
%E A224258 Name corrected by _Andrew Howroyd_, Mar 18 2025