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A295275 T(n,k)=Number of nXk 0..1 arrays with each 1 horizontally or vertically adjacent to 0, 1 or 4 1s. 7

%I

%S 2,4,4,7,11,7,13,33,33,13,24,98,164,98,24,44,291,811,811,291,44,81,

%T 865,4035,6659,4035,865,81,149,2570,19997,54773,54773,19997,2570,149,

%U 274,7637,99245,449827,748740,449827,99245,7637,274,504,22693,492401,3697742

%N T(n,k)=Number of nXk 0..1 arrays with each 1 horizontally or vertically adjacent to 0, 1 or 4 1s.

%C Table starts

%C ...2.....4.......7........13..........24............44..............81

%C ...4....11......33........98.........291...........865............2570

%C ...7....33.....164.......811........4035.........19997...........99245

%C ..13....98.....811......6659.......54773........449827.........3697742

%C ..24...291....4035.....54773......748740......10203847.......139221499

%C ..44...865...19997....449827....10203847.....230659662......5221177246

%C ..81..2570...99245...3697742...139221499....5221177246....196091375073

%C .149..7637..492401..30386185..1898916677..118139247475...7361533108317

%C .274.22693.2443097.249719021.25902054180.2673342943199.276386201580189

%H R. H. Hardin, <a href="/A295275/b295275.txt">Table of n, a(n) for n = 1..419</a>

%F Empirical for column k:

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

%F k=2: a(n) = 2*a(n-1) +3*a(n-2) -a(n-4)

%F k=3: [order 10]

%F k=4: [order 16]

%F k=5: [order 40]

%F k=6: [order 78]

%e Some solutions for n=4 k=4

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

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

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

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

%Y Column 1 is A000073(n+3).

%Y Column 2 is A282990.

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Nov 19 2017

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Last modified October 18 21:56 EDT 2021. Contains 348070 sequences. (Running on oeis4.)