A300973 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3, 4 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

0, 1, 1, 1, 3, 1, 2, 11, 11, 2, 3, 37, 72, 37, 3, 5, 129, 459, 459, 129, 5, 8, 450, 2956, 5362, 2956, 450, 8, 13, 1568, 18996, 63565, 63565, 18996, 1568, 13, 21, 5464, 122043, 753471, 1396701, 753471, 122043, 5464, 21, 34, 19041, 784108, 8926774, 30679527

Offset

1,5

Comments

Table starts

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

..1.....3......11.........37..........129............450..............1568

..1....11......72........459.........2956..........18996............122043

..2....37.....459.......5362........63565.........753471...........8926774

..3...129....2956......63565......1396701.......30679527.........673550354

..5...450...18996.....753471.....30679527.....1248976325.......50812633429

..8..1568..122043....8926774....673550354....50812633429.....3830408271334

.13..5464..784108..105763972..14787165263..2067233940661...288757143760689

.21.19041.5037730.1253091915.324641851765.84103618035068.21768367076769721

Links

R. H. Hardin, Table of n, a(n) for n = 1..241

Formula

Empirical for column k:

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

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

k=3: [order 9] for n>11

k=4: [order 41] for n>42

Example

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

Crossrefs

Column 1 is A000045(n-1).

Column 2 is A232031(n-1).

Sequence in context: A301615 A180771 A300546 * A300930 A109528 A136125

Adjacent sequences: A300970 A300971 A300972 * A300974 A300975 A300976

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 17 2018

Status

approved