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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.

%I A240792 #6 Jun 02 2025 10:00:02
%S A240792 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 A240792 14,24,35,53,82,132,85,50,30,35,54,70,278,552,460,142,89,32,54,83,140,
%U A240792 669,2277,2009,1130,386,115,36,83,124,237,1969,11588,15611,6993,6393,979,182
%N 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.
%C A240792 Table starts
%C A240792 ..2..3...4....7.....10......15.........24.........35..........54.........83
%C A240792 ..3..4...5...10.....14......24.........53.........70.........140........237
%C A240792 ..4..5...8...19.....34......82........278........669........1969.......3553
%C A240792 ..7.10..27...37....132.....552.......2277......11588.......35799.....109054
%C A240792 .10.13..49...85....460....2009......15611......90831......522104....2386511
%C A240792 .15.14..50..142...1130....6993......92681.....983289.....7075546...64616034
%C A240792 .24.30..89..386...6393...69732....1691066...33021579...408482271.5524873850
%C A240792 .35.32.115..979..22255..398128...16946464..651434319.13673101597
%C A240792 .54.36.182.1988..62705.1646410..117913446.8338435721
%C A240792 .83.67.289.5128.252760.9472037.1022475213
%H A240792 R. H. Hardin, <a href="/A240792/b240792.txt">Table of n, a(n) for n = 1..142</a>
%F A240792 Empirical for column k:
%F A240792 k=1: a(n) = a(n-2) +2*a(n-3)
%F A240792 k=2: [order 17] for n>19
%F A240792 k=3: [order 76] for n>87
%F A240792 Empirical for row n:
%F A240792 n=1: a(n) = a(n-2) +2*a(n-3)
%F A240792 n=2: [order 17] for n>21
%e A240792 Some solutions for n=4 k=4
%e A240792 ..3..2..3..2....3..2..3..2....3..2..3..2....3..2..3..3....3..2..3..3
%e A240792 ..3..2..3..2....3..2..1..2....3..2..1..1....3..2..1..1....3..2..1..1
%e A240792 ..2..2..0..3....2..2..0..2....2..2..3..1....2..2..2..2....2..2..3..2
%e A240792 ..2..0..2..2....3..1..3..2....3..1..3..2....3..1..0..2....3..1..3..1
%Y A240792 Row and column 1 are A159288(n+1)
%K A240792 nonn,tabl
%O A240792 1,1
%A A240792 _R. H. Hardin_, Apr 12 2014