|
%I #4 Apr 05 2014 14:24:21
%S 2,4,5,8,21,12,16,89,102,28,32,375,874,476,66,64,1583,7589,8187,2200,
%T 156,128,6685,65723,143237,75167,10123,368,256,28241,568370,2501883,
%U 2632690,682018,46471,868,512,119319,4916340,43654661,92193017,47636104,6147372
%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 three plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest, modulo 4
%C Table starts
%C ....2.......4..........8...........16............32.............64
%C ....5......21.........89..........375..........1583...........6685
%C ...12.....102........874.........7589.........65723.........568370
%C ...28.....476.......8187.......143237.......2501883.......43654661
%C ...66....2200......75167......2632690......92193017.....3228706651
%C ..156...10123.....682018.....47636104....3337483054...234122685500
%C ..368...46471....6147372....854671234..119643524281.16795323356869
%C ..868..213000...55212526..15259447330.4265146133201
%C .2048..975380..494809053.271656519692
%C .4832.4464474.4428808128
%H R. H. Hardin, <a href="/A240460/b240460.txt">Table of n, a(n) for n = 1..84</a>
%F Empirical for column k:
%F k=1: a(n) = 2*a(n-1) +2*a(n-3)
%F k=2: [order 26]
%F Empirical for row n:
%F n=1: a(n) = 2*a(n-1)
%F n=2: a(n) = 6*a(n-1) -7*a(n-2) -4*a(n-3) +8*a(n-4)
%F n=3: [order 23]
%e Some solutions for n=4 k=4
%e ..2..0..0..0....2..2..0..0....0..0..0..2....0..2..2..2....2..2..2..2
%e ..0..0..2..0....2..0..2..0....0..2..0..0....0..0..0..0....2..0..0..0
%e ..0..0..0..0....2..2..2..2....0..0..2..2....0..0..2..0....0..2..2..2
%e ..0..2..2..0....3..1..0..0....0..2..2..2....2..2..2..0....0..2..0..0
%Y Column 1 is A239333
%Y Row 1 is A000079
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Apr 05 2014
| 