|
%I #4 Apr 18 2014 18:17:20
%S 2,2,5,4,6,11,6,15,6,25,8,25,37,12,57,14,40,74,116,16,129,20,89,186,
%T 330,304,28,293,30,121,646,1462,1145,869,38,665,48,237,1278,5757,6718,
%U 4499,2398,66,1509,70,390,3418,22343,49918,41336,15827,6813,92,3425,108,682
%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 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...2.....4......6........8.........14..........20..........30..........48
%C ....5...6....15.....25.......40.........89.........121.........237.........390
%C ...11...6....37.....74......186........646........1278........3418........9113
%C ...25..12...116....330.....1462.......5757.......22343.......79043......304799
%C ...57..16...304...1145.....6718......49918......283985.....1666242.....9581018
%C ..129..28...869...4499....41336.....490486.....5098814....41458261...447396605
%C ..293..38..2398..15827...217785....3893262....70316883...978925384.16677156613
%C ..665..66..6813..58043..1215485...37039909..1194164944.30759996872
%C .1509..92.18782.209838..6526016..307030328.16586413847
%C .3425.154.53067.757771.35833494.2801405991
%H R. H. Hardin, <a href="/A241306/b241306.txt">Table of n, a(n) for n = 1..126</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1) +2*a(n-2) +2*a(n-3)
%F k=2: a(n) = 2*a(n-2) +a(n-3) -a(n-5)
%F Empirical for row n:
%F n=1: a(n) = a(n-2) +2*a(n-3)
%F n=2: [order 14] for n>20
%e Some solutions for n=4 k=4
%e ..3..2..3..2....3..2..3..2....3..2..3..3....3..2..3..2....3..2..2..2
%e ..1..2..1..1....3..1..3..1....1..2..1..1....1..2..1..1....3..0..0..1
%e ..2..0..0..1....1..2..2..3....3..2..2..2....3..2..0..2....1..0..2..1
%e ..1..0..3..3....2..0..0..1....1..2..0..2....2..0..0..3....1..0..0..2
%Y Column 1 is A239812
%Y Row 1 is A239851
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Apr 18 2014
| 