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A316953 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 3, 4, 5, 6 or 7 king-move adjacent elements, with upper left element zero. 7

%I #4 Jul 17 2018 12:25:03

%S 0,1,1,1,7,1,2,25,25,2,3,98,160,98,3,5,383,1240,1240,383,5,8,1493,

%T 9417,18956,9417,1493,8,13,5824,71505,287292,287292,71505,5824,13,21,

%U 22717,543155,4335826,8641499,4335826,543155,22717,21,34,88609,4125662

%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 3, 4, 5, 6 or 7 king-move adjacent elements, with upper left element zero.

%C Table starts

%C ..0.....1........1...........2.............3................5

%C ..1.....7.......25..........98...........383.............1493

%C ..1....25......160........1240..........9417............71505

%C ..2....98.....1240.......18956........287292..........4335826

%C ..3...383.....9417......287292.......8641499........259163370

%C ..5..1493....71505.....4335826.....259163370......15440641209

%C ..8..5824...543155....65510494....7779344498.....920789559090

%C .13.22717..4125662...989703110..233495963949...54906173292280

%C .21.88609.31337363.14951804382.7008276669223.3273992108473660

%H R. H. Hardin, <a href="/A316953/b316953.txt">Table of n, a(n) for n = 1..287</a>

%F Empirical for column k:

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

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

%F k=3: a(n) = 6*a(n-1) +10*a(n-2) +15*a(n-3) +8*a(n-4) +3*a(n-5) +a(n-6) +2*a(n-7)

%F k=4: [order 13]

%F k=5: [order 33]

%F k=6: [order 76]

%e Some solutions for n=5 k=4

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

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

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

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

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

%Y Column 1 is A000045(n-1).

%Y Column 2 is A304421.

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Jul 17 2018

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Last modified March 3 00:46 EST 2024. Contains 370499 sequences. (Running on oeis4.)