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T(n,k)=Number of nXk 0..2 arrays with no element having a strict majority of its horizontal, vertical and antidiagonal neighbors equal to itself plus one mod 3, with upper left element zero (rock paper and scissors drawn positions)
7

%I #4 Nov 14 2013 05:16:20

%S 1,1,1,3,9,3,8,64,64,8,21,439,1205,439,21,55,2992,21770,21770,2992,55,

%T 144,20382,393408,1043604,393408,20382,144,377,138852,7103846,

%U 49913988,49913988,7103846,138852,377,987,945923,128269829,2386203232,6320545103

%N T(n,k)=Number of nXk 0..2 arrays with no element having a strict majority of its horizontal, vertical and antidiagonal neighbors equal to itself plus one mod 3, with upper left element zero (rock paper and scissors drawn positions)

%C Table starts

%C ...1......1..........3.............8................21...................55

%C ...1......9.........64...........439..............2992................20382

%C ...3.....64.......1205.........21770............393408..............7103846

%C ...8....439......21770.......1043604..........49913988...........2386203232

%C ..21...2992.....393408......49913988........6320545103.........800089656653

%C ..55..20382....7103846....2386203232......800089656653......268201160539247

%C .144.138852..128269829..114066364087...101271407955316....89898324366354186

%C .377.945923.2316065437.5452552422721.12818259615003968.30132701233909614426

%H R. H. Hardin, <a href="/A231828/b231828.txt">Table of n, a(n) for n = 1..112</a>

%F Empirical for column k:

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

%F k=2: a(n) = 9*a(n-1) -16*a(n-2) +11*a(n-3) -27*a(n-4) +21*a(n-5) -4*a(n-6)

%F k=3: [order 36] for n>37

%e Some solutions for n=3 k=4

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

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

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

%Y Column 1 is A001906(n-1)

%K nonn,tabl

%O 1,4

%A _R. H. Hardin_, Nov 14 2013