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A224029 Number of 7Xn 0..3 arrays with rows nondecreasing and antidiagonals unimodal.

%I A224029 #6 Jul 23 2025 04:54:44
%S A224029 16384,10000000,508916456,9186127249,99853876444,800511624819,
%T A224029 5173325036371,28312680063277,135506470642023,580135646807494,
%U A224029 2259103048155965,8104442812190513,27055697058861926,84736180130576912
%N A224029 Number of 7Xn 0..3 arrays with rows nondecreasing and antidiagonals unimodal.
%C A224029 Row 7 of A224024
%H A224029 R. H. Hardin, <a href="/A224029/b224029.txt">Table of n, a(n) for n = 1..210</a>
%F A224029 Empirical: a(n) = (3642102403/12772735542927360000)*n^21 + (1828819507/93573154160640000)*n^20 + (69800896237/91233825306624000)*n^19 + (267473506319/12804747411456000)*n^18 + (13894779382807/32011868528640000)*n^17 + (30522003341/4269957120000)*n^16 + (2960783594047/30893806944000)*n^15 + (396044918673407/376610217984000)*n^14 + (53677409656497673/5649153269760000)*n^13 + (20242631281245749/289700167680000)*n^12 + (2982742874548721/7242504192000)*n^11 + (1737409609193009/919683072000)*n^10 + (258559348958260442861/39544072888320000)*n^9 + (593900455377212143/36212520960000)*n^8 + (3978525082857841027/141228831744000)*n^7 + (1946054065487953843/47076277248000)*n^6 + (49893145987491754499/666913927680000)*n^5 - (383268963922742041/1984862880000)*n^4 - (252880325219600223869/123193822752000)*n^3 - (154838552783847197/36664828200)*n^2 + (12390598682741/2909907)*n + 3399959 for n>5
%e A224029 Some solutions for n=3
%e A224029 ..0..0..0....0..0..0....0..0..0....0..0..0....0..0..0....0..0..0....0..0..0
%e A224029 ..0..0..0....0..0..0....0..0..0....0..0..0....0..0..0....0..0..0....0..0..0
%e A224029 ..0..0..2....0..0..2....0..0..2....0..2..2....0..0..0....0..0..2....0..0..0
%e A224029 ..2..2..2....2..2..3....2..2..2....0..0..1....2..2..2....2..2..2....1..2..2
%e A224029 ..0..2..3....0..2..3....0..0..2....0..0..3....2..2..3....1..1..1....0..2..2
%e A224029 ..2..2..3....1..3..3....0..1..1....0..3..3....1..2..2....1..1..3....0..1..2
%e A224029 ..1..2..3....2..3..3....0..1..2....2..2..2....0..2..3....0..0..1....1..2..3
%K A224029 nonn
%O A224029 1,1
%A A224029 _R. H. Hardin_ Mar 30 2013