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A223766 Number of n X 4 0..1 arrays with rows, columns and antidiagonals unimodal and diagonals nondecreasing.

%I A223766 #10 Jul 23 2025 04:29:25
%S A223766 11,56,155,361,782,1601,3141,5907,10678,18618,31422,51505,82243,
%T A223766 128276,195884,293448,432009,625939,893739,1258980,1751404,2408203,
%U A223766 3275495,4410017,5881056,7772640,10186012,13242411,17086185,21888262,27850006
%N A223766 Number of n X 4 0..1 arrays with rows, columns and antidiagonals unimodal and diagonals nondecreasing.
%C A223766 Column 4 of A223770.
%H A223766 R. H. Hardin, <a href="/A223766/b223766.txt">Table of n, a(n) for n = 1..210</a>
%F A223766 Empirical: a(n) = (1/40320)*n^8 - (1/10080)*n^7 + (3/320)*n^6 + (1/45)*n^5 + (1109/1920)*n^4 - (4837/1440)*n^3 + (422483/10080)*n^2 - (109337/840)*n + 226 for n>4.
%F A223766 Conjectures from _Colin Barker_, Aug 22 2018: (Start)
%F A223766 G.f.: x*(11 - 43*x + 47*x^2 + 58*x^3 - 205*x^4 + 209*x^5 - 42*x^6 - 150*x^7 + 256*x^8 - 245*x^9 + 151*x^10 - 55*x^11 + 9*x^12) / (1 - x)^9.
%F A223766 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>13.
%F A223766 (End)
%e A223766 Some solutions for n=3:
%e A223766 ..1..1..1..0....0..0..1..1....0..0..1..0....1..0..0..0....0..1..1..0
%e A223766 ..0..1..1..1....0..1..1..1....1..1..1..1....0..1..0..0....0..1..1..1
%e A223766 ..0..1..1..1....1..1..1..1....1..1..1..1....0..0..1..1....0..0..1..1
%Y A223766 Cf. A223770.
%K A223766 nonn
%O A223766 1,1
%A A223766 _R. H. Hardin_, Mar 27 2013