The On-Line Encyclopedia of Integer Sequences (OEIS)

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A304149

T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 3 or 6 king-move adjacent elements, with upper left element zero.
(history; published version)

#4 by R. H. Hardin at Mon May 07 08:56:14 EDT 2018

STATUS

editing

approved

#3 by R. H. Hardin at Mon May 07 08:56:10 EDT 2018

LINKS

R. H. Hardin, <a href="/A304149/b304149.txt">Table of n, a(n) for n = 1..264</a>

#2 by R. H. Hardin at Mon May 07 08:55:54 EDT 2018

NAME

allocated for R. H. Hardin

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

DATA

0, 1, 1, 1, 7, 1, 2, 14, 14, 2, 3, 33, 18, 33, 3, 5, 70, 25, 25, 70, 5, 8, 157, 113, 61, 113, 157, 8, 13, 346, 238, 157, 157, 238, 346, 13, 21, 769, 359, 117, 1198, 117, 359, 769, 21, 34, 1710, 1309, 244, 3484, 3484, 244, 1309, 1710, 34, 55, 3813, 3091, 936, 5336, 13152

OFFSET

1,5

COMMENTS

Table starts

..0....1....1...2.....3......5......8.......13........21........34.........55

..1....7...14..33....70....157....346......769......1710......3813.......8514

..1...14...18..25...113....238....359.....1309......3091......5173......15475

..2...33...25..61...157....117....244......936.......733......1513.......5788

..3...70..113.157..1198...3484...5336....24401.....90422....181207.....546435

..5..157..238.117..3484..13152..12582...139840....774023...1302357....5969791

..8..346..359.244..5336..12582...6492...218516....748819....579549....8291908

.13..769.1309.936.24401.139840.218516..1429403..12033436..34502082..116115677

.21.1710.3091.733.90422.774023.748819.12033436.180869894.471888374.2046852451

FORMULA

Empirical for column k:

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

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

k=3: [order 14] for n>16

k=4: [order 17] for n>22

k=5: [order 93] for n>96

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

CROSSREFS

Column 1 is A000045(n-1).

KEYWORD

allocated

nonn,tabl

AUTHOR

R. H. Hardin, May 07 2018

STATUS

approved

editing

#1 by R. H. Hardin at Mon May 07 08:49:47 EDT 2018

NAME

allocated for R. H. Hardin

KEYWORD

allocated

STATUS

approved