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A296320 T(n,k)=Number of nXk 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 1 neighboring 1. 7

%I

%S 1,2,2,3,6,3,4,11,11,4,6,27,32,27,6,9,60,96,96,60,9,13,132,295,434,

%T 295,132,13,19,301,902,1970,1970,902,301,19,28,669,2747,8470,12547,

%U 8470,2747,669,28,41,1502,8380,37431,77426,77426,37431,8380,1502,41,60,3370,25577

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

%C Table starts

%C ..1....2.....3......4........6.........9..........13...........19............28

%C ..2....6....11.....27.......60.......132.........301..........669..........1502

%C ..3...11....32.....96......295.......902........2747.........8380.........25577

%C ..4...27....96....434.....1970......8470.......37431.......164807........723019

%C ..6...60...295...1970....12547.....77426......490668......3078638......19343899

%C ..9..132...902...8470....77426....676269.....6069953.....54182821.....482859661

%C .13..301..2747..37431...490668...6069953....78105580....994666167...12644605701

%C .19..669..8380.164807..3078638..54182821...994666167..18043360170..326902733082

%C .28.1502.25577.723019.19343899.482859661.12644605701.326902733082.8435284786616

%H R. H. Hardin, <a href="/A296320/b296320.txt">Table of n, a(n) for n = 1..544</a>

%F Empirical for column k:

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

%F k=2: a(n) = a(n-1) +2*a(n-2) +2*a(n-3) -a(n-4) +a(n-5)

%F k=3: a(n) = a(n-1) +4*a(n-2) +6*a(n-3) +3*a(n-4) -3*a(n-6) +a(n-7) -3*a(n-9) +a(n-11)

%F k=4: [order 21]

%F k=5: [order 43]

%F k=6: [order 85]

%e Some solutions for n=5 k=4

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

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

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

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

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

%Y Column 1 is A000930(n+1).

%Y Column 2 is A184884(n+1).

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Dec 10 2017

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Last modified February 28 01:15 EST 2020. Contains 332319 sequences. (Running on oeis4.)