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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
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, 295, 132, 13, 19, 301, 902, 1970, 1970, 902, 301, 19, 28, 669, 2747, 8470, 12547, 8470, 2747, 669, 28, 41, 1502, 8380, 37431, 77426, 77426, 37431, 8380, 1502, 41, 60, 3370, 25577 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Table starts

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

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

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

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

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

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

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

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

.28.1502.25577.723019.19343899.482859661.12644605701.326902733082.8435284786616

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..544

FORMULA

Empirical for column k:

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

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

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)

k=4: [order 21]

k=5: [order 43]

k=6: [order 85]

EXAMPLE

Some solutions for n=5 k=4

..0..0..0..0. .1..0..0..0. .0..0..0..0. .0..0..1..0. .0..0..0..0

..0..0..0..0. .1..0..0..0. .0..0..0..0. .0..0..1..0. .1..1..0..0

..1..0..0..0. .0..1..1..0. .0..0..1..0. .0..0..0..0. .0..0..1..0

..1..0..0..1. .0..0..0..1. .0..1..0..0. .0..1..0..1. .0..1..0..0

..0..0..0..1. .1..1..0..1. .0..0..0..0. .0..1..0..1. .0..0..1..1

CROSSREFS

Column 1 is A000930(n+1).

Column 2 is A184884(n+1).

Sequence in context: A272958 A290632 A291543 * A296396 A125102 A003506

Adjacent sequences:  A296317 A296318 A296319 * A296321 A296322 A296323

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Dec 10 2017

STATUS

approved

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Last modified January 21 11:11 EST 2020. Contains 331105 sequences. (Running on oeis4.)