A300639 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 4 or 5 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

0, 1, 1, 1, 2, 1, 2, 6, 6, 2, 3, 15, 13, 15, 3, 5, 37, 34, 34, 37, 5, 8, 90, 91, 97, 91, 90, 8, 13, 223, 253, 300, 300, 253, 223, 13, 21, 550, 705, 1036, 1130, 1036, 705, 550, 21, 34, 1355, 1978, 3313, 4418, 4418, 3313, 1978, 1355, 34, 55, 3341, 5507, 11075, 17607, 23097

Offset

1,5

Comments

Table starts

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

..1....2....6....15.....37......90......223.......550.......1355........3341

..1....6...13....34.....91.....253......705......1978.......5507.......15222

..2...15...34....97....300....1036.....3313.....11075......37067......122922

..3...37...91...300...1130....4418....17607.....71861.....297729.....1239693

..5...90..253..1036...4418...23097...124439....666648....3654138....20086516

..8..223..705..3313..17607..124439...865205...6105466...44264248...319622847

.13..550.1978.11075..71861..666648..6105466..57365508..551242313..5228508530

.21.1355.5507.37067.297729.3654138.44264248.551242313.7042663221.88534058107

Links

R. H. Hardin, Table of n, a(n) for n = 1..220

Formula

Empirical for column k:

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

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

k=3: [order 32]

Example

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

Crossrefs

Column 1 is A000045(n-1).

Column 2 is A300344.

Sequence in context: A300350 A300435 A300769 * A301361 A267864 A336524

Adjacent sequences: A300636 A300637 A300638 * A300640 A300641 A300642

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 10 2018

Status

approved