cp's OEIS Frontend

A224043 Number of 7 X n 0..1 arrays with antidiagonals unimodal and rows and diagonals nondecreasing.

%I A224043 #8 Aug 26 2018 17:00:20
%S A224043 128,987,2419,4160,6321,9125,12856,17875,24623,33686,45837,62087,
%T A224043 83746,112495,150470,200359,265513,350072,459107,598779,776516,
%U A224043 1001209,1283428,1635659,2072563,2611258,3271625,4076639,5052726,6230147,7643410,9331711
%N A224043 Number of 7 X n 0..1 arrays with antidiagonals unimodal and rows and diagonals nondecreasing.
%C A224043 Row 7 of A224038.
%H A224043 R. H. Hardin, <a href="/A224043/b224043.txt">Table of n, a(n) for n = 1..210</a>
%F A224043 Empirical: a(n) = (1/5040)*n^7 + (17/360)*n^5 + (13/24)*n^4 + (5767/720)*n^3 + (1919/24)*n^2 + (37901/70)*n + 143 for n>5.
%F A224043 Conjectures from _Colin Barker_, Aug 26 2018: (Start)
%F A224043 G.f.: x*(128 - 37*x - 1893*x^2 + 5276*x^3 - 5539*x^4 + 1495*x^5 + 1526*x^6 - 1101*x^7 + 65*x^8 + 155*x^9 - 160*x^10 + 117*x^11 - 31*x^12) / (1 - x)^8.
%F A224043 a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>13.
%F A224043 (End)
%e A224043 Some solutions for n=3:
%e A224043 ..0..1..1....0..0..0....1..1..1....0..0..0....1..1..1....0..0..1....0..0..0
%e A224043 ..0..0..1....1..1..1....0..1..1....0..1..1....0..1..1....0..1..1....0..0..0
%e A224043 ..0..1..1....1..1..1....0..0..1....0..0..1....0..0..1....1..1..1....0..0..0
%e A224043 ..1..1..1....1..1..1....0..1..1....0..1..1....0..0..1....0..1..1....0..0..1
%e A224043 ..0..1..1....0..1..1....0..0..1....1..1..1....0..0..1....0..1..1....0..1..1
%e A224043 ..0..0..1....0..1..1....0..0..0....0..1..1....0..0..0....1..1..1....0..0..1
%e A224043 ..0..0..1....0..0..1....0..0..0....0..1..1....0..0..0....0..1..1....0..0..0
%Y A224043 Cf. A224038.
%K A224043 nonn
%O A224043 1,1
%A A224043 _R. H. Hardin_, Mar 30 2013