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A240271 T(n,k)=Number of nXk 0..3 arrays with no element equal to zero plus the sum of elements to its left or one plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest, modulo 4.

%I A240271 #6 Jun 02 2025 09:45:19
%S A240271 2,4,3,10,7,4,24,35,14,7,56,157,118,36,10,132,713,919,582,72,15,312,
%T A240271 3263,7562,8265,2000,170,24,736,14895,64721,126286,49921,8353,411,35,
%U A240271 1736,68101,563496,2059061,1363144,382690,37422,879,54,4096,311509,4956889
%N A240271 T(n,k)=Number of nXk 0..3 arrays with no element equal to zero plus the sum of elements to its left or one plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest, modulo 4.
%C A240271 Table starts
%C A240271 ..2....4......10.........24..........56..........132...........312
%C A240271 ..3....7......35........157.........713.........3263.........14895
%C A240271 ..4...14.....118........919........7562........64721........563496
%C A240271 ..7...36.....582.......8265......126286......2059061......34514871
%C A240271 .10...72....2000......49921.....1363144.....40760821....1277623744
%C A240271 .15..170....8353.....382690....19210586...1063706501...63085436203
%C A240271 .24..411...37422....3076452...278945445..27923918285.3004792552569
%C A240271 .35..879..135463...19781372..3200032085.576407548906
%C A240271 .54.2106..580528..154994425.46095401280
%C A240271 .83.4874.2403439.1144262410
%H A240271 R. H. Hardin, <a href="/A240271/b240271.txt">Table of n, a(n) for n = 1..97</a>
%F A240271 Empirical for column k:
%F A240271 k=1: a(n) = a(n-2) +2*a(n-3)
%F A240271 k=2: [order 13]
%F A240271 Empirical for row n:
%F A240271 n=1: a(n) = 2*a(n-1) +2*a(n-3)
%F A240271 n=2: [order 26] for n>28
%e A240271 Some solutions for n=4 k=4
%e A240271 ..2..3..0..3....3..2..2..2....3..0..0..2....3..0..2..0....3..2..2..2
%e A240271 ..2..1..2..3....3..1..2..1....2..3..2..0....2..3..0..2....2..1..2..0
%e A240271 ..2..0..1..0....2..1..2..2....3..1..2..0....3..1..1..0....3..2..0..2
%e A240271 ..2..0..1..0....2..0..0..1....3..2..2..0....3..2..2..1....2..3..2..2
%Y A240271 Column 1 is A159288(n+1)
%Y A240271 Row 1 is A052912
%K A240271 nonn,tabl
%O A240271 1,1
%A A240271 _R. H. Hardin_, Apr 03 2014