cp's OEIS Frontend

A275565 T(n,k)=Number of nXk 0..2 arrays with no element equal to any value at offset (-2,0) (-1,2) or (0,-2) and new values introduced in order 0..2.

%I A275565 #4 Aug 01 2016 21:28:19
%S A275565 1,2,2,3,14,3,6,36,54,6,12,96,126,216,12,24,288,294,504,864,24,48,864,
%T A275565 672,1176,1872,3456,48,96,2592,1536,3192,4056,7200,13824,96,192,7776,
%U A275565 3552,8664,13104,15000,27360,55296,192,384,23328,8214,23712,42336,57600
%N A275565 T(n,k)=Number of nXk 0..2 arrays with no element equal to any value at offset (-2,0) (-1,2) or (0,-2) and new values introduced in order 0..2.
%C A275565 Table starts
%C A275565 ...1......2.......3.......6.......12........24.........48..........96
%C A275565 ...2.....14......36......96......288.......864.......2592........7776
%C A275565 ...3.....54.....126.....294......672......1536.......3552........8214
%C A275565 ...6....216.....504....1176.....3192......8664......23712.......64896
%C A275565 ..12....864....1872....4056....13104.....42336.....138600......453750
%C A275565 ..24...3456....7200...15000....57600....221184.....867456.....3402054
%C A275565 ..48..13824...27360...54150...248520...1140576....5360184....25190406
%C A275565 ..96..55296..104256..196566..1075140...5880600...33275880...188294424
%C A275565 .192.221184..397440..714150..4663710..30456054..206892990..1405458150
%C A275565 .384.884736.1513728.2589894.20186982.157347846.1286374716.10516571736
%H A275565 R. H. Hardin, <a href="/A275565/b275565.txt">Table of n, a(n) for n = 1..286</a>
%F A275565 Empirical for column k:
%F A275565 k=1: a(n) = 2*a(n-1) for n>3
%F A275565 k=2: a(n) = 4*a(n-1) for n>3
%F A275565 k=3: a(n) = 2*a(n-1) +8*a(n-2) -16*a(n-4) for n>5
%F A275565 k=4: [order 10] for n>11
%F A275565 k=5: [order 32] for n>34
%F A275565 k=6: [order 35] for n>37
%F A275565 Empirical for row n:
%F A275565 n=1: a(n) = 2*a(n-1) for n>3
%F A275565 n=2: a(n) = 3*a(n-1) for n>4
%F A275565 n=3: a(n) = 3*a(n-1) -5*a(n-3) +a(n-4) +7*a(n-5) -5*a(n-6) +2*a(n-8) -a(n-9) for n>10
%F A275565 n=4: [order 25] for n>28
%F A275565 n=5: [order 63] for n>66
%e A275565 Some solutions for n=4 k=4
%e A275565 ..0..1..2..2. .0..1..1..2. .0..1..2..2. .0..1..2..0. .0..1..2..0
%e A275565 ..1..0..0..1. .0..1..2..0. .1..0..0..2. .0..1..1..2. .1..1..2..2
%e A275565 ..2..2..1..1. .1..2..2..1. .1..0..0..1. .2..0..1..1. .1..0..0..2
%e A275565 ..2..2..1..0. .1..0..0..1. .2..2..1..1. .2..2..0..1. .2..0..0..1
%Y A275565 Column 1 is A003945(n-2).
%Y A275565 Column 2 is A208428.
%Y A275565 Row 1 is A003945(n-2).
%K A275565 nonn,tabl
%O A275565 1,2
%A A275565 _R. H. Hardin_, Aug 01 2016