The On-Line Encyclopedia of Integer Sequences (OEIS)

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A302889

T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3, 4 or 5 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
(history; published version)

#4 by R. H. Hardin at Sun Apr 15 10:50:18 EDT 2018

STATUS

editing

approved

#3 by R. H. Hardin at Sun Apr 15 10:50:14 EDT 2018

LINKS

R. H. Hardin, <a href="/A302889/b302889.txt">Table of n, a(n) for n = 1..180</a>

#2 by R. H. Hardin at Sun Apr 15 10:49:57 EDT 2018

NAME

allocated for R. H. Hardin

T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3, 4 or 5 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

DATA

1, 1, 2, 1, 2, 4, 1, 12, 2, 8, 1, 20, 37, 3, 16, 1, 72, 53, 141, 6, 32, 1, 168, 197, 238, 569, 10, 64, 1, 496, 818, 2278, 1102, 2262, 21, 128, 1, 1296, 2548, 12782, 20937, 5570, 8968, 42, 256, 1, 3616, 10926, 98458, 200186, 206332, 28594, 35667, 86, 512, 1, 9760, 42671

OFFSET

1,3

COMMENTS

Table starts

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

...2..2.....12.....20........72.........168...........496............1296

...4..2.....37.....53.......197.........818..........2548...........10926

...8..3....141....238......2278.......12782.........98458..........714934

..16..6....569...1102.....20937......200186.......2727690........37626360

..32.10...2262...5570....206332.....3452246......89290791......2247650354

..64.21...8968..28594...2059835....60501563....2899297652....133518102376

.128.42..35667.149206..20622709..1073161270...94799190457...7977498513759

.256.86.141839.788373.206851726.19073141368.3098646840396.476377988322833

FORMULA

Empirical for column k:

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

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

k=3: [order 10]

k=4: [order 35] for n>37

Empirical for row n:

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

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

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

n=4: [order 51] for n>54

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

CROSSREFS

Column 1 is A000079(n-1).

Column 2 is A240513(n-2).

Row 2 is A302368.

KEYWORD

allocated

nonn,tabl

AUTHOR

R. H. Hardin, Apr 15 2018

STATUS

approved

editing

#1 by R. H. Hardin at Sun Apr 15 10:45:05 EDT 2018

NAME

allocated for R. H. Hardin

KEYWORD

allocated

STATUS

approved