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Number of nX4 0..2 arrays with no element equal to any value at offset (0,-1) (-1,-2) or (-2,0) and new values introduced in order 0..2.
1

%I #4 Jul 14 2016 09:50:05

%S 4,48,137,570,2334,9774,40572,169348,704704,2937764,12236817,50996499,

%T 212474695,885374358,3689111563,15371973010,64051973628,266893366673,

%U 1112095776824,4633902454111,19308634583221,80455590398414

%N Number of nX4 0..2 arrays with no element equal to any value at offset (0,-1) (-1,-2) or (-2,0) and new values introduced in order 0..2.

%C Column 4 of A275037.

%H R. H. Hardin, <a href="/A275033/b275033.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 4*a(n-1) +14*a(n-2) -62*a(n-3) -40*a(n-4) +388*a(n-5) -306*a(n-6) -1193*a(n-7) +2504*a(n-8) +1764*a(n-9) -7620*a(n-10) -1306*a(n-11) +13370*a(n-12) +1805*a(n-13) -16980*a(n-14) -5291*a(n-15) +18277*a(n-16) +10135*a(n-17) -18477*a(n-18) -12333*a(n-19) +18384*a(n-20) +9126*a(n-21) -15323*a(n-22) -4234*a(n-23) +9693*a(n-24) +1188*a(n-25) -4598*a(n-26) -61*a(n-27) +1605*a(n-28) -135*a(n-29) -382*a(n-30) +68*a(n-31) +53*a(n-32) -14*a(n-33) -3*a(n-34) +a(n-35) for n>37

%e Some solutions for n=4

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

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

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

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

%Y Cf. A275037.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jul 14 2016