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R. H. Hardin, <a href="/A232920/b232920.txt">Table of n, a(n) for n = 1..391</a>

allocated for R. H. Hardin

T(n,k)=Number of nXk 0..2 arrays with no element x(i,j) adjacent to value 2-x(i,j) horizontally, diagonally or antidiagonally

3, 6, 9, 12, 18, 27, 24, 54, 54, 81, 48, 144, 246, 162, 243, 96, 396, 912, 1122, 486, 729, 192, 1080, 3612, 5808, 5118, 1458, 2187, 384, 2952, 13992, 33702, 37008, 23346, 4374, 6561, 768, 8064, 54600, 186720, 316800, 235824, 106494, 13122, 19683, 1536, 22032

1,1

Table starts

.....3......6.......12........24..........48............96............192

.....9.....18.......54.......144.........396..........1080...........2952

....27.....54......246.......912........3612.........13992..........54600

....81....162.....1122......5808.......33702........186720........1054446

...243....486.....5118.....37008......316800.......2515716.......20706696

...729...1458....23346....235824.....2986152......33994188......409408542

..2187...4374...106494...1502736....28178262.....459797904.....8119777890

..6561..13122...485778...9575856...266016264....6221092260...161274860934

.19683..39366..2215902..61020048..2511769872...84180552504..3205524631536

.59049.118098.10107954.388836912.23718269934.1139126465856.63736076920680

Empirical for column k:

k=1: a(n) = 3*a(n-1)

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

k=3: a(n) = 5*a(n-1) -2*a(n-2)

k=4: a(n) = 7*a(n-1) -4*a(n-2)

k=5: a(n) = 14*a(n-1) -45*a(n-2) +15*a(n-3) +36*a(n-4) -19*a(n-5) +2*a(n-6)

k=6: [order 9]

k=7: [order 19]

Empirical for row n:

n=1: a(n) = 2*a(n-1)

n=2: a(n) = 2*a(n-1) +2*a(n-2)

n=3: a(n) = 3*a(n-1) +4*a(n-2) -2*a(n-3) for n>4

n=4: a(n) = 3*a(n-1) +16*a(n-2) -3*a(n-3) -25*a(n-4) +2*a(n-5) +4*a(n-6) for n>7

n=5: [order 10] for n>11

n=6: [order 23] for n>24

n=7: [order 46] for n>47

Some solutions for n=4 k=4

..0..0..1..0....0..0..1..0....0..0..1..0....0..0..1..0....1..0..0..1

..0..0..1..2....0..0..1..2....1..0..1..0....1..0..1..0....1..0..0..1

..1..0..1..2....0..0..1..0....1..0..1..2....0..0..1..2....0..0..0..0

..0..0..1..2....0..0..0..0....0..0..1..0....1..0..1..2....1..0..1..0

Column 1 is A000244

Column 2 is A008776

Column 3 is A206144(n-1) for n>2

Column 4 is A223373

Row 1 is A003945

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R. H. Hardin, Dec 02 2013

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