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A238812 T(n,k)=Number of nXk 0..2 arrays with no element equal to one plus the sum of elements to its left or one plus the sum of the elements above it, modulo 3 8

%I #4 Mar 05 2014 17:33:59

%S 2,3,3,4,8,4,5,15,15,5,6,25,48,25,6,7,39,118,118,39,7,8,58,254,468,

%T 254,58,8,9,83,498,1501,1501,498,83,9,10,115,916,4167,7502,4167,916,

%U 115,10,11,155,1605,10423,31125,31125,10423,1605,155,11,12,204,2702,24115

%N T(n,k)=Number of nXk 0..2 arrays with no element equal to one plus the sum of elements to its left or one plus the sum of the elements above it, modulo 3

%C Table starts

%C ..2...3....4......5.......6........7..........8...........9...........10

%C ..3...8...15.....25......39.......58.........83.........115..........155

%C ..4..15...48....118.....254......498........916........1605.........2702

%C ..5..25..118....468....1501.....4167......10423.......24115........52449

%C ..6..39..254...1501....7502....31125.....111564......356666......1041746

%C ..7..58..498...4167...31125...197418....1055763.....4880856.....19977948

%C ..8..83..916..10423..111564..1055763....8526852....58670336....348923836

%C ..9.115.1605..24115..356666..4880856...58670336...605163204...5342432459

%C .10.155.2702..52449.1041746.19977948..348923836..5342432459..70386525080

%C .11.204.4395.108395.2828429.73988808.1828642499.40798150971.796431939717

%H R. H. Hardin, <a href="/A238812/b238812.txt">Table of n, a(n) for n = 1..312</a>

%F k=1: a(n) = n + 1

%F k=2: a(n) = (1/6)*n^3 + (23/6)*n - 1

%F k=3: [polynomial of degree 6] for n>2

%F k=4: [polynomial of degree 10] for n>4

%F k=5: [polynomial of degree 15] for n>6

%F k=6: [polynomial of degree 21] for n>8

%F k=7: [polynomial of degree 28] for n>10

%e Some solutions for n=5 k=4

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

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

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

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

%e ..2..2..0..0....0..0..0..0....0..0..2..2....2..2..0..1....0..0..0..0 Empirical for column k:

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Mar 05 2014

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Last modified June 21 13:19 EDT 2024. Contains 373544 sequences. (Running on oeis4.)