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A224395 Number of 6Xn 0..3 arrays with diagonals and antidiagonals unimodal and rows nondecreasing.

%I A224395 #6 Jul 23 2025 05:09:22
%S A224395 4096,1000000,18794636,152271025,879830242,4364554008,19879000458,
%T A224395 84675848787,337896379016,1262027034092,4414609771988,14497401758306,
%U A224395 44849313719663,131213360082438,364483316826362,964981060109623
%N A224395 Number of 6Xn 0..3 arrays with diagonals and antidiagonals unimodal and rows nondecreasing.
%C A224395 Row 6 of A224391
%H A224395 R. H. Hardin, <a href="/A224395/b224395.txt">Table of n, a(n) for n = 1..96</a>
%F A224395 Empirical: a(n) = (42587101/1600593426432000)*n^18 + (83940121/177843714048000)*n^17 + (351548291/31384184832000)*n^16 + (404522743/2615348736000)*n^15 + (2603179801/1426553856000)*n^14 + (13975516589/747242496000)*n^13 + (1018677008761/3621252096000)*n^12 - (71772294491/67060224000)*n^11 + (9590385658061/219469824000)*n^10 - (19294207174217/73156608000)*n^9 + (6061000683461531/2414168064000)*n^8 - (67636294337629/7185024000)*n^7 + (580563104944166119/11769069312000)*n^6 + (14843452118300317/653837184000)*n^5 - (42702408306785177/59439744000)*n^4 + (14422633437701933/3027024000)*n^3 - (272645035897423741/15437822400)*n^2 + (10375478018905/1225224)*n + 82732433 for n>10
%e A224395 Some solutions for n=3
%e A224395 ..0..0..0....0..0..0....0..0..0....0..0..0....0..0..0....0..0..0....0..0..0
%e A224395 ..0..0..0....0..0..2....0..0..2....0..0..2....0..0..0....0..0..2....0..0..2
%e A224395 ..0..2..3....0..2..2....2..2..3....0..2..2....2..2..2....2..2..2....0..2..2
%e A224395 ..0..3..3....0..2..3....0..2..3....2..2..2....0..2..2....2..2..3....0..2..3
%e A224395 ..1..2..3....0..0..1....0..1..1....0..2..3....1..3..3....2..2..3....3..3..3
%e A224395 ..1..3..3....0..0..2....0..2..3....0..0..1....0..1..1....0..0..1....0..2..2
%K A224395 nonn
%O A224395 1,1
%A A224395 _R. H. Hardin_ Apr 05 2013