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A250994 T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with nondecreasing min(x(i,j),x(i,j-1)) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction 16

%I

%S 40,169,158,646,872,612,2359,4007,4111,2323,8298,16993,21955,18387,

%T 8726,28450,67409,104674,111175,80133,32554,95628,255502,456514,

%U 590305,542834,344135,120930,316568,934786,1869400,2800667,3184615,2592734,1466191

%N T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with nondecreasing min(x(i,j),x(i,j-1)) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction

%C Table starts

%C ......40.......169........646........2359........8298........28450

%C .....158.......872.......4007.......16993.......67409.......255502

%C .....612......4111......21955......104674......456514......1869400

%C ....2323.....18387.....111175......590305.....2800667.....12340547

%C ....8726.....80133.....542834.....3184615....16381510.....77449279

%C ...32554....344135....2592734....16694358....92713991....469255626

%C ..120930...1466191...12238954....86049801...514669302...2783159034

%C ..447985...6219851...57388086...438901153..2820364768..16265322280

%C .1656600..26329263..268220043..2225675881.15340901571..94211007762

%C .6118822.111352239.1251995646.11253642389.83091814176.542676800586

%H R. H. Hardin, <a href="/A250994/b250994.txt">Table of n, a(n) for n = 1..180</a>

%F Empirical for column k:

%F k=1: a(n) = 6*a(n-1) -7*a(n-2) -8*a(n-3) +7*a(n-4) +6*a(n-5) +a(n-6)

%F k=2: [order 12]

%F k=3: [order 20]

%F k=4: [order 33]

%F k=5: [order 51]

%F k=6: [order 78]

%F Empirical for row n:

%F n=1: a(n) = 6*a(n-1) -7*a(n-2) -12*a(n-3) +15*a(n-4) +11*a(n-5) -5*a(n-6) -3*a(n-7)

%F n=2: [order 14]

%F n=3: [order 23]

%F n=4: [order 34]

%F n=5: [order 43] for n>45

%F n=6: [order 54] for n>58

%F n=7: [order 67] for n>73

%e Some solutions for n=3 k=4

%e ..1..2..0..2..0....0..0..1..0..2....1..0..0..0..1....0..1..0..2..0

%e ..1..2..0..2..0....0..1..0..1..0....1..0..0..1..0....1..0..1..0..2

%e ..1..2..0..1..2....0..2..1..0..2....1..1..1..2..1....1..0..1..0..2

%e ..1..2..0..1..1....1..1..2..1..0....1..1..2..1..2....1..0..1..2..0

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Nov 29 2014

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Last modified October 25 10:46 EDT 2021. Contains 348239 sequences. (Running on oeis4.)