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A223836 Number of n X 6 0..1 arrays with rows, diagonals and antidiagonals unimodal and columns nondecreasing.

%I A223836 #10 Mar 18 2025 20:54:05
%S A223836 22,148,503,1286,2884,5992,11749,21912,39064,66854,110269,175938,
%T A223836 272468,410812,604669,870916,1230072,1706794,2330405,3135454,4162308,
%U A223836 5457776,7075765,9077968,11534584,14525070,18138925,22476506,27649876,33783684
%N A223836 Number of n X 6 0..1 arrays with rows, diagonals and antidiagonals unimodal and columns nondecreasing.
%H A223836 R. H. Hardin, <a href="/A223836/b223836.txt">Table of n, a(n) for n = 1..210</a>
%F A223836 Empirical: a(n) = (2/45)*n^6 + (55/36)*n^4 + (14/3)*n^3 + (3767/180)*n^2 + (293/6)*n - 116 for n>3.
%F A223836 Conjectures from _Colin Barker_, Aug 23 2018: (Start)
%F A223836 G.f.: x*(22 - 6*x - 71*x^2 + 103*x^3 + 35*x^4 - 77*x^5 + 10*x^6 + 22*x^7 - 4*x^8 - 2*x^9) / (1 - x)^7.
%F A223836 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>10.
%F A223836 (End)
%e A223836 Some solutions for n=3:
%e A223836 ..0..0..0..0..0..1....0..1..1..0..0..0....0..0..0..0..0..0....0..0..0..1..1..0
%e A223836 ..0..0..1..1..1..1....1..1..1..1..0..0....0..1..0..0..0..0....0..0..0..1..1..0
%e A223836 ..1..1..1..1..1..1....1..1..1..1..1..1....1..1..1..1..1..1....0..0..1..1..1..1
%Y A223836 Column 6 of A223838.
%K A223836 nonn
%O A223836 1,1
%A A223836 _R. H. Hardin_, Mar 27 2013
%E A223836 Name corrected by _Andrew Howroyd_, Mar 18 2025