A302877 - OEIS

A302877

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

1, 2, 2, 3, 3, 4, 5, 11, 6, 8, 8, 21, 17, 10, 16, 13, 31, 35, 37, 21, 32, 21, 113, 72, 95, 82, 42, 64, 34, 363, 241, 306, 285, 209, 86, 128, 55, 813, 722, 1442, 1197, 858, 536, 179, 256, 89, 1751, 1821, 5871, 7580, 4849, 2938, 1549, 370, 512, 144, 5001, 4863, 21832, 41498

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Table starts

...1...2....3.....5......8.......13........21..........34...........55

...2...3...11....21.....31......113.......363.........813.........1751

...4...6...17....35.....72......241.......722........1821.........4863

...8..10...37....95....306.....1442......5871.......21832........89400

..16..21...82...285...1197.....7580.....41498......224087......1300510

..32..42..209...858...4849....45897....359518.....2795440.....24612087

..64..86..536..2938..23037...320405...3780984....44148194....588417750

.128.179.1549.11126.114810..2489823..44888558...786125894..15974455418

.256.370.4513.44216.603229.20679119.569313013.14827387374.460770487307

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..180

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 13] for n>16

k=4: [order 56] for n>59

Empirical for row n:

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

n=2: a(n) = 2*a(n-1) -a(n-2) +4*a(n-3) +12*a(n-4) -16*a(n-5) for n>6

n=3: [order 20] for n>21

n=4: [order 60] for n>64

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

CROSSREFS

Column 1 is A000079(n-1).

Column 2 is A240513.

Row 1 is A000045(n+1).

Row 2 is A302310.

Sequence in context: A059185 A302309 A303040 * A303525 A368643 A133948

Adjacent sequences: A302874 A302875 A302876 * A302878 A302879 A302880

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Apr 15 2018

STATUS

approved