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A240792 T(n,k)=Number of nXk 0..3 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 or zero plus the sum of the elements diagonally to its northwest or zero plus the sum of the elements antidiagonally to its northeast, modulo 4 7

%I #4 Apr 12 2014 19:12:51

%S 2,3,3,4,4,4,7,5,5,7,10,10,8,10,10,15,14,19,27,13,15,24,24,34,37,49,

%T 14,24,35,53,82,132,85,50,30,35,54,70,278,552,460,142,89,32,54,83,140,

%U 669,2277,2009,1130,386,115,36,83,124,237,1969,11588,15611,6993,6393,979,182

%N T(n,k)=Number of nXk 0..3 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 or zero plus the sum of the elements diagonally to its northwest or zero plus the sum of the elements antidiagonally to its northeast, modulo 4

%C Table starts

%C ..2..3...4....7.....10......15.........24.........35..........54.........83

%C ..3..4...5...10.....14......24.........53.........70.........140........237

%C ..4..5...8...19.....34......82........278........669........1969.......3553

%C ..7.10..27...37....132.....552.......2277......11588.......35799.....109054

%C .10.13..49...85....460....2009......15611......90831......522104....2386511

%C .15.14..50..142...1130....6993......92681.....983289.....7075546...64616034

%C .24.30..89..386...6393...69732....1691066...33021579...408482271.5524873850

%C .35.32.115..979..22255..398128...16946464..651434319.13673101597

%C .54.36.182.1988..62705.1646410..117913446.8338435721

%C .83.67.289.5128.252760.9472037.1022475213

%H R. H. Hardin, <a href="/A240792/b240792.txt">Table of n, a(n) for n = 1..142</a>

%F Empirical for column k:

%F k=1: a(n) = a(n-2) +2*a(n-3)

%F k=2: [order 17] for n>19

%F k=3: [order 76] for n>87

%F Empirical for row n:

%F n=1: a(n) = a(n-2) +2*a(n-3)

%F n=2: [order 17] for n>21

%e Some solutions for n=4 k=4

%e ..3..2..3..2....3..2..3..2....3..2..3..2....3..2..3..3....3..2..3..3

%e ..3..2..3..2....3..2..1..2....3..2..1..1....3..2..1..1....3..2..1..1

%e ..2..2..0..3....2..2..0..2....2..2..3..1....2..2..2..2....2..2..3..2

%e ..2..0..2..2....3..1..3..2....3..1..3..2....3..1..0..2....3..1..3..1

%Y Row and column 1 are A159288(n+1)

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Apr 12 2014

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Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)