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A224005 Number of 7Xn 0..2 arrays with antidiagonals unimodal and rows and diagonals nondecreasing.

%I A224005 #6 Jul 23 2025 04:50:01
%S A224005 2187,102069,739672,2743444,7400832,16795265,34534687,67029572,
%T A224005 125640165,230434296,416688642,746070578,1325631005,2339607173,
%U A224005 4101879980,7141164265,12337189420,21134985710,35876879602,60309132371,100343859256
%N A224005 Number of 7Xn 0..2 arrays with antidiagonals unimodal and rows and diagonals nondecreasing.
%C A224005 Row 7 of A223999
%H A224005 R. H. Hardin, <a href="/A224005/b224005.txt">Table of n, a(n) for n = 1..210</a>
%F A224005 Empirical: a(n) = (1/203212800)*n^14 + (1/29030400)*n^13 + (817/319334400)*n^12 + (2627/63866880)*n^11 + (8279/9676800)*n^10 + (408523/29030400)*n^9 + (46918247/203212800)*n^8 + (17877667/5806080)*n^7 + (73580257/1814400)*n^6 + (1465470497/3628800)*n^5 + (385797089/100800)*n^4 + (7741678111/362880)*n^3 + (387997970341/3880800)*n^2 - (400735465/1386)*n - 1233287 for n>10
%e A224005 Some solutions for n=3
%e A224005 ..0..0..0....0..0..0....0..0..0....0..0..0....0..0..0....0..0..0....0..0..0
%e A224005 ..1..1..1....0..0..1....0..0..1....0..1..1....0..1..1....1..2..2....1..2..2
%e A224005 ..0..1..2....0..0..1....0..1..1....1..2..2....0..1..2....0..2..2....0..1..2
%e A224005 ..0..2..2....0..1..1....0..1..2....0..1..2....0..1..1....1..1..2....0..1..1
%e A224005 ..0..0..2....1..1..2....1..1..2....1..1..1....0..0..2....0..1..1....0..0..2
%e A224005 ..0..1..2....0..1..2....0..1..2....0..1..2....0..0..2....0..2..2....0..0..2
%e A224005 ..0..0..2....0..1..1....0..1..1....0..2..2....0..2..2....2..2..2....0..2..2
%K A224005 nonn
%O A224005 1,1
%A A224005 _R. H. Hardin_ Mar 30 2013