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A223639 Number of n X 3 0..1 arrays with rows, columns, diagonals and antidiagonals unimodal.

%I A223639 #8 Aug 22 2018 06:25:26
%S A223639 7,49,218,726,2014,4904,10797,21917,41601,74635,127636,209480,331776,
%T A223639 509386,760991,1109703,1583723,2217045,3050206,4131082,5515730,
%U A223639 7269276,9466849,12194561,15550533,19645967,24606264,30572188,37701076,46168094
%N A223639 Number of n X 3 0..1 arrays with rows, columns, diagonals and antidiagonals unimodal.
%C A223639 Column 3 of A223644.
%H A223639 R. H. Hardin, <a href="/A223639/b223639.txt">Table of n, a(n) for n = 1..210</a>
%F A223639 Empirical: a(n) = (23/360)*n^6 - (3/40)*n^5 + (31/18)*n^4 + (5/8)*n^3 + (1517/360)*n^2 - (51/20)*n + 3.
%F A223639 Conjectures from _Colin Barker_, Aug 22 2018: (Start)
%F A223639 G.f.: x*(7 + 22*x^2 - 16*x^3 + 40*x^4 - 10*x^5 + 3*x^6) / (1 - x)^7.
%F A223639 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 A223639 (End)
%e A223639 Some solutions for n=4:
%e A223639 ..0..1..1....1..1..0....0..0..0....0..1..0....0..1..1....0..1..0....0..0..1
%e A223639 ..0..1..1....1..1..0....1..1..0....1..1..0....1..1..0....1..1..0....0..0..1
%e A223639 ..1..1..0....1..1..0....1..1..0....0..1..1....0..0..0....1..1..0....0..1..1
%e A223639 ..1..0..0....0..0..1....0..0..1....0..0..1....0..0..0....1..0..0....0..1..1
%Y A223639 Cf. A223644.
%K A223639 nonn
%O A223639 1,1
%A A223639 _R. H. Hardin_, Mar 24 2013