A304010 - OEIS

A304010

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

1, 1, 1, 1, 4, 1, 1, 7, 7, 1, 1, 13, 13, 13, 1, 1, 26, 21, 21, 26, 1, 1, 49, 27, 26, 27, 49, 1, 1, 99, 53, 64, 64, 53, 99, 1, 1, 194, 99, 115, 137, 115, 99, 194, 1, 1, 387, 197, 211, 271, 271, 211, 197, 387, 1, 1, 773, 371, 439, 655, 538, 655, 439, 371, 773, 1, 1, 1538, 713, 870

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OFFSET

1,5

COMMENTS

Table starts

.1...1...1...1....1....1.....1.....1......1......1.......1.......1........1

.1...4...7..13...26...49....99...194....387....773....1538....3081.....6147

.1...7..13..21...27...53....99...197....371....713....1365....2645.....5105

.1..13..21..26...64..115...211...439....870...1725....3513....7141....14372

.1..26..27..64..137..271...655..1412...3245...7809...17290...40682....93292

.1..49..53.115..271..538..1458..2973...7826..19113...47074..115148...283156

.1..99..99.211..655.1458..4224.10633..28365..75175..201031..544217..1452266

.1.194.197.439.1412.2973.10633.30468..84398.254233..751747.2193664..6512888

.1.387.371.870.3245.7826.28365.84398.264104.857398.2706019.8591303.27513653

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..264

FORMULA

Empirical for column k:

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

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

k=3: [order 16] for n>17

k=4: [order 67] for n>70

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

CROSSREFS

Sequence in context: A304141 A305047 A316733 * A305360 A304952 A316620

Adjacent sequences: A304007 A304008 A304009 * A304011 A304012 A304013

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, May 04 2018

STATUS

approved