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A224042 Number of 6 X n 0..1 arrays with antidiagonals unimodal and rows and diagonals nondecreasing.

%I A224042 #10 Jul 23 2025 04:56:24
%S A224042 64,377,848,1422,2149,3107,4395,6124,8439,11527,15626,21035,28125,
%T A224042 37351,49265,64530,83935,108411,139048,177113,224069,281595,351607,
%U A224042 436280,538071,659743,804390,975463,1176797,1412639,1687677,2007070,2376479
%N A224042 Number of 6 X n 0..1 arrays with antidiagonals unimodal and rows and diagonals nondecreasing.
%C A224042 Row 6 of A224038.
%H A224042 R. H. Hardin, <a href="/A224042/b224042.txt">Table of n, a(n) for n = 1..210</a>
%F A224042 Empirical: a(n) = (1/720)*n^6 + (1/240)*n^5 + (35/144)*n^4 + (127/48)*n^3 + (1249/45)*n^2 + (3727/20)*n + 6 for n>4.
%F A224042 Conjectures from _Colin Barker_, Aug 26 2018: (Start)
%F A224042 G.f.: x*(64 - 71*x - 447*x^2 + 1163*x^3 - 952*x^4 + 97*x^5 + 216*x^6 - 72*x^7 + 33*x^8 - 45*x^9 + 15*x^10) / (1 - x)^7.
%F A224042 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>11.
%F A224042 (End)
%e A224042 Some solutions for n=3:
%e A224042 ..0..0..0....1..1..1....1..1..1....0..0..0....0..0..0....0..0..0....1..1..1
%e A224042 ..0..0..1....0..1..1....1..1..1....1..1..1....0..0..0....0..0..0....0..1..1
%e A224042 ..0..0..0....0..1..1....0..1..1....1..1..1....0..0..0....0..0..0....0..0..1
%e A224042 ..0..0..1....0..1..1....0..1..1....0..1..1....0..0..0....0..0..1....0..0..1
%e A224042 ..0..0..0....1..1..1....0..1..1....1..1..1....0..0..1....0..1..1....0..0..0
%e A224042 ..0..1..1....1..1..1....1..1..1....0..1..1....0..1..1....1..1..1....0..0..0
%Y A224042 Cf. A224038.
%K A224042 nonn
%O A224042 1,1
%A A224042 _R. H. Hardin_, Mar 30 2013