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A224040 Number of 4 X n 0..1 arrays with antidiagonals unimodal and rows and diagonals nondecreasing.

%I A224040 #8 Aug 26 2018 11:11:25
%S A224040 16,55,105,168,252,363,508,695,933,1232,1603,2058,2610,3273,4062,4993,
%T A224040 6083,7350,8813,10492,12408,14583,17040,19803,22897,26348,30183,34430,
%U A224040 39118,44277,49938,56133,62895,70258,78257,86928,96308,106435,117348
%N A224040 Number of 4 X n 0..1 arrays with antidiagonals unimodal and rows and diagonals nondecreasing.
%C A224040 Row 4 of A224038.
%H A224040 R. H. Hardin, <a href="/A224040/b224040.txt">Table of n, a(n) for n = 1..210</a>
%F A224040 Empirical: a(n) = (1/24)*n^4 + (1/4)*n^3 + (83/24)*n^2 + (89/4)*n - 3 for n>2.
%F A224040 Conjectures from _Colin Barker_, Aug 26 2018: (Start)
%F A224040 G.f.: x*(16 - 25*x - 10*x^2 + 33*x^3 - 8*x^4 - 8*x^5 + 3*x^6) / (1 - x)^5.
%F A224040 a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>7.
%F A224040 (End)
%e A224040 Some solutions for n=3:
%e A224040 ..1..1..1....1..1..1....0..0..1....0..1..1....0..0..1....0..0..0....1..1..1
%e A224040 ..1..1..1....0..1..1....1..1..1....0..1..1....1..1..1....0..0..1....0..1..1
%e A224040 ..1..1..1....0..1..1....0..1..1....0..1..1....1..1..1....1..1..1....0..0..1
%e A224040 ..0..1..1....0..1..1....0..0..1....0..0..1....1..1..1....0..1..1....0..0..1
%Y A224040 Cf. A224038.
%K A224040 nonn
%O A224040 1,1
%A A224040 _R. H. Hardin_, Mar 30 2013