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A224353 T(n,k)=Number of nXk 0..2 arrays with diagonals and antidiagonals unimodal and rows nondecreasing.

%I A224353 #6 Jul 23 2025 05:06:57
%S A224353 3,6,9,10,36,27,15,100,216,81,21,225,788,1296,243,28,441,2321,5880,
%T A224353 7776,729,36,784,5840,19608,45064,46656,2187,45,1296,13052,57387,
%U A224353 160362,349280,279936,6561,55,2025,26610,151010,495985,1351748,2710892,1679616
%N A224353 T(n,k)=Number of nXk 0..2 arrays with diagonals and antidiagonals unimodal and rows nondecreasing.
%C A224353 Table starts
%C A224353 .....3........6.........10.........15..........21..........28...........36
%C A224353 .....9.......36........100........225.........441.........784.........1296
%C A224353 ....27......216........788.......2321........5840.......13052........26610
%C A224353 ....81.....1296.......5880......19608.......57387......151010.......363392
%C A224353 ...243.....7776......45064.....160362......495985.....1421762......3816783
%C A224353 ...729....46656.....349280....1351748.....4231138....12340932.....34697869
%C A224353 ..2187...279936....2710892...11704964....37433596...107694133....300892325
%C A224353 ..6561..1679616...21021916..102319662...342170839...977742699...2654062881
%C A224353 .19683.10077696..163012744..895494806..3178789749..9202126546..24422915139
%C A224353 .59049.60466176.1264202660.7833508842.29672959682.88363107023.233364588801
%H A224353 R. H. Hardin, <a href="/A224353/b224353.txt">Table of n, a(n) for n = 1..264</a>
%F A224353 Empirical: columns k=1..6 have recurrences of order 1,1,10,26,56,98
%F A224353 Empirical: rows n=1..7 are polynomials of degree 2*n for k>0,0,1,3,5,7,9
%e A224353 Some solutions for n=3 k=4
%e A224353 ..1..1..1..2....0..0..1..1....0..0..2..2....1..2..2..2....0..2..2..2
%e A224353 ..1..1..1..2....0..0..2..2....0..1..1..2....0..1..2..2....1..1..2..2
%e A224353 ..0..0..1..2....0..1..1..1....0..1..1..2....1..2..2..2....1..1..1..2
%Y A224353 Column 1 is A000244
%Y A224353 Column 2 is A000400
%Y A224353 Row 1 is A000217(n+1)
%Y A224353 Row 2 is A000537(n+1)
%K A224353 nonn,tabl
%O A224353 1,1
%A A224353 _R. H. Hardin_ Apr 04 2013