A300612 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3 or 5 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

0, 1, 1, 1, 3, 1, 2, 10, 10, 2, 3, 30, 53, 30, 3, 5, 96, 277, 277, 96, 5, 8, 307, 1432, 2347, 1432, 307, 8, 13, 981, 7514, 19532, 19532, 7514, 981, 13, 21, 3137, 39330, 164619, 263468, 164619, 39330, 3137, 21, 34, 10034, 205958, 1387896, 3567928, 3567928

Offset

1,5

Comments

Table starts

..0.....1.......1........2..........3............5..............8

..1.....3......10.......30.........96..........307............981

..1....10......53......277.......1432.........7514..........39330

..2....30.....277.....2347......19532.......164619........1387896

..3....96....1432....19532.....263468......3567928.......48279880

..5...307....7514...164619....3567928.....77669371.....1693172810

..8...981...39330..1387896...48279880...1693172810....59556673490

.13..3137..205958.11697909..653282566..36914891724..2093683166397

.21.10034.1078479.98591087.8839456244.804586936082.73570793306416

Links

R. H. Hardin, Table of n, a(n) for n = 1..199

Formula

Empirical for column k:

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

k=2: a(n) = 3*a(n-1) +a(n-2) -3*a(n-4) -2*a(n-5) -a(n-6) for n>7

k=3: [order 17] for n>18

k=4: [order 72] for n>73

Example

Some solutions for n=5 k=4
..0..0..0..0. .0..1..1..0. .0..0..0..1. .0..1..0..0. .0..0..0..0
..0..1..0..1. .0..1..0..0. .1..0..0..1. .0..1..1..0. .0..1..1..0
..0..1..0..1. .1..0..1..0. .1..1..0..0. .0..0..1..1. .0..0..1..1
..0..1..0..0. .1..0..1..0. .1..0..1..0. .0..1..0..1. .1..0..0..1
..1..0..1..1. .0..0..0..0. .0..1..1..0. .1..1..0..0. .1..1..0..0

Crossrefs

Column 1 is A000045(n-1).

Column 2 is A300421.

Sequence in context: A301669 A300427 A300689 * A301354 A229187 A126226

Adjacent sequences: A300609 A300610 A300611 * A300613 A300614 A300615

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 09 2018

Status

approved