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A250691 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 absolute value of x(i,j)-x(i-1,j) in the j direction.

%I A250691 #8 Jul 23 2025 12:42:03
%S A250691 104,543,520,2541,2920,2512,11150,13906,15246,11736,47002,60508,74631,
%T A250691 76320,53032,193117,249512,324648,383440,362241,233300,780551,995624,
%U A250691 1315446,1670016,1848953,1647460,1005121,3122604,3894542,5098590,6671458
%N A250691 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 absolute value of x(i,j)-x(i-1,j) in the j direction.
%C A250691 Table starts
%C A250691 ......104.......543.......2541.......11150.......47002......193117......780551
%C A250691 ......520......2920......13906.......60508......249512......995624.....3894542
%C A250691 .....2512.....15246......74631......324648.....1315446.....5098590....19218493
%C A250691 ....11736.....76320.....383440.....1670016.....6671458....25235016....92169818
%C A250691 ....53032....362241....1848953.....8038566....31728758...117793753...420283865
%C A250691 ...233300...1647460....8474002....36673634...143136866...523260542..1832718604
%C A250691 ..1005121...7249825...37322413...160222342...617657415..2224688673..7662909389
%C A250691 ..4260728..31113316..159438246...676640344..2571646112..9121206688.30911828018
%C A250691 .17835379.131014715..665575403..2784280670.10412478449.36332194553
%C A250691 .73930174.543845812.2731006288.11235235268.41269021168
%H A250691 R. H. Hardin, <a href="/A250691/b250691.txt">Table of n, a(n) for n = 1..112</a>
%F A250691 Empirical for column k:
%F A250691 k=1: [linear recurrence of order 7] for n>11
%F A250691 k=2: [order 13] for n>17
%F A250691 k=3: [same order 13] for n>17
%F A250691 k=4: [same order 13] for n>17
%F A250691 k=5: [same order 13] for n>17
%F A250691 k=6: [same order 13] for n>17
%F A250691 k=7: [same order 13] for n>17
%F A250691 Empirical for row n:
%F A250691 n=1: [linear recurrence of order 7, cf. A250692]
%F A250691 n=2: [order 10, cf. A250693]
%F A250691 n=3: [order 16, cf. A250694]
%F A250691 n=4: [same order 16, cf. A250695]
%F A250691 n=5: [same order 16, cf. A250696]
%F A250691 n=6: [same order 16, cf. A250697]
%F A250691 n=7: [same order 16, cf. A250698].
%e A250691 Some solutions for n=3 k=4
%e A250691 ..2..3..1..0..0....2..2..3..2..2....2..2..1..1..0....0..1..0..0..0
%e A250691 ..2..3..2..1..1....0..0..1..0..0....2..2..2..2..3....0..1..0..0..1
%e A250691 ..1..2..1..0..0....0..0..1..1..1....1..1..1..1..2....1..2..1..1..2
%e A250691 ..0..1..2..1..3....0..0..1..1..2....0..0..0..0..3....1..2..1..1..2
%Y A250691 Column 1 is A250669.
%Y A250691 Rows 1-7 are A250692, ..., A250698.
%K A250691 nonn,tabl
%O A250691 1,1
%A A250691 _R. H. Hardin_, Nov 26 2014