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%I #16 Mar 12 2015 22:40:24
%S 150,1080,1080,6627,10704,6627,36552,79366,79366,36552,187000,491650,
%T 644779,491650,187000,905440,2701872,4169584,4169584,2701872,905440,
%U 4206453,13657024,23289547,27240292,23289547,13657024,4206453,18933408
%N T(n,k) = number of (n+1)X(k+1) 0..3 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing x(i,j)-x(i-1,j) in the j direction.
%C _Peter Luschny_ remarks that the coefficients of the empirical recurrence relation for the column 1 are listed in the 9th row of A246117. - _M. F. Hasler_, Feb 11 2015
%H R. H. Hardin, <a href="/A250544/b250544.txt">Table of n, a(n) for n = 1..144</a>
%F Empirical for column k (k=2-7 recurrence also works for k=1):
%F k=1: a(n) = 16*a(n-1) -106*a(n-2) +376*a(n-3) -769*a(n-4) +904*a(n-5) -564*a(n-6) +144*a(n-7)
%F k=2: [order 16, see A250538]
%F k=3: [same order 16]
%F k=4: [same order 16]
%F k=5: [same order 16]
%F k=6: [same order 16]
%F k=7: [same order 16]
%e Some solutions for n=2 k=4
%e ..2..2..1..0..0....2..0..3..1..1....2..2..2..2..0....0..0..2..0..0
%e ..2..3..2..2..2....0..0..3..2..2....2..2..2..2..0....1..1..3..1..1
%e ..1..3..2..3..3....0..0..3..2..3....1..2..2..2..3....0..0..2..0..2
%e Table starts:
%e .......150.......1080........6627........36552........187000........905440
%e ......1080......10704.......79366.......491650.......2701872......13657024
%e ......6627......79366......644779......4169584......23289547.....117777788
%e .....36552.....491650.....4169584.....27240292.....151170400.....752602024
%e ....187000....2701872....23289547....151170400.....824599694....4013192386
%e ....905440...13657024...117777788....752602024....4013192386...19031828420
%e ...4206453...64993652...555362165...3475227442...18064444143...83356429646
%e ..18933408..295871112..2489782728..15210145612...76961701472..345394150196
%e ..83153850.1302924116.10756619019..64036997144..315204675572.1375930596944
%e .358250280.5595784456.45218540866.262068107390.1254564769204.5328628464360
%Y Row/column 1 is A223069(n+1) and row/column 2 of A223071.
%Y Row/column 2-7 are A250538 - A250543; diagonal is A250537.
%Y See also A250676, A250669 - A250675, A250691, A250692...
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Nov 24 2014
%E Edited by _M. F. Hasler_, Feb 11 2015
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