A240422 - OEIS

%I #4 Apr 04 2014 18:33:41

%S 3,7,7,15,35,15,31,147,147,31,63,553,1161,553,63,127,2045,7857,7857,

%T 2045,127,255,7439,52711,97269,52711,7439,255,511,27099,347155,

%U 1197511,1197511,347155,27099,511,1023,98193,2331517,14516959,27488435,14516959

%N T(n,k)=Number of nXk 0..3 arrays with no element equal to two plus the sum of elements to its left or two 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 ....3.......7........15..........31...........63...........127...........255

%C ....7......35.......147.........553.........2045..........7439.........27099

%C ...15.....147......1161........7857........52711........347155.......2331517

%C ...31.....553......7857.......97269......1197511......14516959.....182716785

%C ...63....2045.....52711.....1197511.....27488435.....619040901...14838256141

%C ..127....7439....347155....14516959....619040901...26075879845.1191246174665

%C ..255...27099...2331517...182716785..14838256141.1191246174665

%C ..511...98193..15537761..2283795777.349768244657

%C .1023..356367.105095051.29455167803

%C .2047.1290555.706172043

%H R. H. Hardin, <a href="/A240422/b240422.txt">Table of n, a(n) for n = 1..84</a>

%F Empirical for column k:

%F k=1: a(n) = 3*a(n-1) -2*a(n-2)

%F k=2: [order 15]

%F k=3: [order 96] for n>100

%e Some solutions for n=4 k=4

%e ..3..3..1..3....1..1..1..0....0..0..1..1....3..3..1..0....3..0..0..0

%e ..3..0..0..2....1..0..1..1....0..3..0..2....3..0..0..0....0..0..3..0

%e ..3..0..2..2....1..1..2..1....0..0..0..0....1..0..2..3....0..1..2..3

%e ..1..0..0..0....0..1..1..3....0..3..0..3....3..0..0..0....0..1..0..2

%Y Column 1 is A000225(n+1)

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Apr 04 2014