|
%I #4 Apr 04 2014 20:57:20
%S 2,2,2,4,6,4,4,24,24,4,8,58,206,58,8,8,236,970,970,236,8,16,566,8084,
%T 9036,8084,566,16,16,2322,38406,150350,150350,38406,2322,16,32,5578,
%U 319164,1404008,5087802,1404008,319164,5578,32,32,22912,1514122,23414762
%N T(n,k)=Number of nXk 0..3 arrays with no element equal to zero plus the sum of elements to its left or zero plus the sum of the elements above it or two plus the sum of the elements diagonally to its northwest, modulo 4
%C Table starts
%C ..2.....2........4...........4..............8...............8...............16
%C ..2.....6.......24..........58............236.............566.............2322
%C ..4....24......206.........970...........8084...........38406...........319164
%C ..4....58......970........9036.........150350.........1404008.........23414762
%C ..8...236.....8084......150350........5087802........94860720.......3184383016
%C ..8...566....38406.....1404008.......94860720......3523795084.....237034323164
%C .16..2322...319164....23414762.....3184383016....237034323164...32020507274002
%C .16..5578..1514122...218412550....59125702284...8779074387924.2372829502697230
%C .32.22912.12567490..3639548326..1979684295626.589446737374098
%C .32.55054.59600672.33928317272.36705060609854
%H R. H. Hardin, <a href="/A240433/b240433.txt">Table of n, a(n) for n = 1..111</a>
%F Empirical for column k:
%F k=1: a(n) = 2*a(n-2)
%F k=2: a(n) = 12*a(n-2) -24*a(n-4) +31*a(n-6) -16*a(n-8)
%F k=3: [order 48]
%e Some solutions for n=4 k=4
%e ..3..1..1..3....1..3..3..1....1..3..3..1....1..3..3..1....1..3..3..1
%e ..1..2..2..2....3..2..2..0....3..2..2..0....3..2..2..0....3..0..2..2
%e ..1..2..1..3....1..0..0..0....3..0..0..0....3..2..0..2....3..0..2..0
%e ..3..2..3..2....3..2..0..3....1..2..2..0....1..0..2..0....1..0..2..0
%Y Column 1 is A016116(n+1)
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Apr 04 2014
| 