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 A304347 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 4 or 5 king-move adjacent elements, with upper left element zero. 8

%I #4 May 11 2018 14:16:56

%S 1,2,2,4,4,4,8,14,14,8,16,28,27,28,16,32,94,71,71,94,32,64,284,225,

%T 290,225,284,64,128,752,613,1266,1266,613,752,128,256,2244,1752,4733,

%U 6373,4733,1752,2244,256,512,6532,5102,18855,27505,27505,18855,5102,6532,512

%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 4 or 5 king-move adjacent elements, with upper left element zero.

%C Table starts

%C ...1....2.....4......8......16.......32........64........128.........256

%C ...2....4....14.....28......94......284.......752.......2244........6532

%C ...4...14....27.....71.....225......613......1752.......5102.......14673

%C ...8...28....71....290....1266.....4733.....18855......76887......308978

%C ..16...94...225...1266....6373....27505....127511.....633229.....3052998

%C ..32..284...613...4733...27505...135445....741942....4355191....24554331

%C ..64..752..1752..18855..127511...741942...4921043...36193582...250785575

%C .128.2244..5102..76887..633229..4355191..36193582..343449680..2937754820

%C .256.6532.14673.308978.3052998.24554331.250785575.2937754820.30008468246

%H R. H. Hardin, <a href="/A304347/b304347.txt">Table of n, a(n) for n = 1..219</a>

%F Empirical for column k:

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

%F k=2: a(n) = 2*a(n-1) +2*a(n-2) +6*a(n-3) -10*a(n-4) -8*a(n-5) for n>6

%F k=3: [order 15] for n>16

%F k=4: [order 57] for n>60

%e Some solutions for n=5 k=4

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

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

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

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

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

%Y Column 1 is A000079(n-1).

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, May 11 2018

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Last modified December 6 09:20 EST 2023. Contains 367600 sequences. (Running on oeis4.)