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A241349 T(n,k)=Number of nXk 0..3 arrays with no element equal to the same number of vertical neighbors as horizontal neighbors, with new values 0..3 introduced in row major order 5

%I #4 Apr 19 2014 18:31:30

%S 0,1,1,1,2,1,2,5,5,2,3,22,36,22,3,6,103,415,415,103,6,11,519,4671,

%T 10998,4671,519,11,23,2656,56166,295782,295782,56166,2656,23,47,13798,

%U 670557,8216943,18750240,8216943,670557,13798,47,102,72005,8072717,229552661

%N T(n,k)=Number of nXk 0..3 arrays with no element equal to the same number of vertical neighbors as horizontal neighbors, with new values 0..3 introduced in row major order

%C Table starts

%C ...0......1..........1............2.............3..............6.............11

%C ...1......2..........5...........22...........103............519...........2656

%C ...1......5.........36..........415..........4671..........56166.........670557

%C ...2.....22........415........10998........295782........8216943......229552661

%C ...3....103.......4671.......295782......18750240.....1223251170....80178068077

%C ...6....519......56166......8216943....1223251170...187086636654.28781500332998

%C ..11...2656.....670557....229552661...80178068077.28781500332998

%C ..23..13798....8072717...6440926150.5272889838441

%C ..47..72005...97173041.180941958872

%C .102.377132.1170969462

%H R. H. Hardin, <a href="/A241349/b241349.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) +a(n-2) -7*a(n-3) +a(n-4) +3*a(n-5) for n>6

%F k=2: [order 10] for n>11

%F k=3: [order 46] for n>47

%e Some solutions for n=4 k=4

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

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

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

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

%Y Column 1 is A199142

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Apr 19 2014

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Last modified March 1 14:57 EST 2024. Contains 370433 sequences. (Running on oeis4.)