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A274895 T(n,k)=Number of nXk 0..2 arrays with no element equal to any value at offset (0,-1) (-1,-1) or (-2,0) and new values introduced in order 0..2.

%I A274895 #4 Jul 10 2016 20:01:11
%S A274895 1,1,2,2,4,3,4,12,7,6,8,36,16,14,12,16,108,37,38,26,24,32,324,86,104,
%T A274895 84,50,48,64,972,200,290,275,192,95,96,128,2916,465,815,913,753,436,
%U A274895 181,192,256,8748,1081,2291,3064,3017,2049,990,345,384,512,26244,2513,6434,10337
%N A274895 T(n,k)=Number of nXk 0..2 arrays with no element equal to any value at offset (0,-1) (-1,-1) or (-2,0) and new values introduced in order 0..2.
%C A274895 Table starts
%C A274895 ...1...1....2.....4......8......16.......32........64........128.........256
%C A274895 ...2...4...12....36....108.....324......972......2916.......8748.......26244
%C A274895 ...3...7...16....37.....86.....200......465......1081.......2513........5842
%C A274895 ...6..14...38...104....290.....815.....2291......6434......18065.......50729
%C A274895 ..12..26...84...275....913....3064....10337.....34921.....117975......398560
%C A274895 ..24..50..192...753...3017...12217....49697....202749.....828828.....3391310
%C A274895 ..48..95..436..2049...9863...48269...237807...1173787....5803040....28746995
%C A274895 ..96.181..990..5602..32539..191974..1143185...6843349...41072451...246859250
%C A274895 .192.345.2253.15305.107369..767905..5539989..40156061..292253909..2133745005
%C A274895 .384.657.5121.41866.354366.3065418.26833885.236220817.2086382703.18485204565
%H A274895 R. H. Hardin, <a href="/A274895/b274895.txt">Table of n, a(n) for n = 1..420</a>
%F A274895 Empirical for column k:
%F A274895 k=1: a(n) = 2*a(n-1) for n>3
%F A274895 k=2: a(n) = a(n-1) +2*a(n-2) -a(n-4) for n>5
%F A274895 k=3: a(n) = a(n-1) +4*a(n-2) -6*a(n-4) -a(n-5) +4*a(n-6) -a(n-8) for n>10
%F A274895 k=4: [order 16] for n>18
%F A274895 k=5: [order 32] for n>34
%F A274895 k=6: [order 64] for n>66
%F A274895 Empirical for row n:
%F A274895 n=1: a(n) = 2*a(n-1) for n>2
%F A274895 n=2: a(n) = 3*a(n-1) for n>2
%F A274895 n=3: a(n) = 3*a(n-1) -2*a(n-2) +a(n-3)
%F A274895 n=4: a(n) = 5*a(n-1) -9*a(n-2) +10*a(n-3) -6*a(n-4) +a(n-5) for n>6
%F A274895 n=5: [order 8] for n>9
%F A274895 n=6: [order 13] for n>14
%F A274895 n=7: [order 21] for n>22
%e A274895 Some solutions for n=4 k=4
%e A274895 ..0..1..0..2. .0..1..2..0. .0..1..0..2. .0..1..2..0. .0..1..2..1
%e A274895 ..2..1..2..1. .1..2..0..1. .2..1..0..2. .1..2..0..1. .1..2..0..1
%e A274895 ..1..0..2..1. .2..0..1..2. .1..0..2..1. .1..2..1..2. .1..0..1..2
%e A274895 ..1..0..1..0. .2..0..1..0. .1..0..2..0. .2..0..1..2. .2..0..1..0
%Y A274895 Column 1 is A003945(n-2).
%Y A274895 Column 2 is A052535(n+1).
%Y A274895 Row 1 is A000079(n-2).
%Y A274895 Row 2 is A003946(n-1).
%Y A274895 Row 3 is A010912(n-1).
%K A274895 nonn,tabl
%O A274895 1,3
%A A274895 _R. H. Hardin_, Jul 10 2016