A301964 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1 or 4 horizontally or antidiagonally adjacent elements, with upper left element zero.

1, 2, 2, 3, 5, 4, 5, 6, 13, 8, 8, 9, 16, 34, 16, 13, 14, 25, 40, 89, 32, 21, 22, 41, 64, 100, 233, 64, 34, 35, 74, 111, 169, 252, 610, 128, 55, 56, 132, 219, 311, 441, 632, 1597, 256, 89, 90, 239, 443, 749, 874, 1156, 1588, 4181, 512, 144, 145, 437, 904, 1803, 2544, 2454

Offset

1,2

Comments

Table starts

...1....2....3....5.....8.....13.....21......34.......55........89.......144

...2....5....6....9....14.....22.....35......56.......90.......145.......234

...4...13...16...25....41.....74....132.....239......437.......800......1468

...8...34...40...64...111....219....443.....904.....1860......3856......8015

..16...89..100..169...311....749...1803....4257....10353.....25491.....62623

..32..233..252..441...874...2544...7795...22456....66659....203926....621905

..64..610..632.1156..2454...8705..33860..120603...444357...1715911...6574776

.128.1597.1588.3025..6906..29750.148299..655332..3014296..14863160..72345489

.256.4181.3988.7921.19427.101869.646838.3557239.20467528.129324707.802690313

Links

R. H. Hardin, Table of n, a(n) for n = 1..880

Formula

Empirical for column k:

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

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

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

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

k=5: a(n) = 2*a(n-1) +3*a(n-2) -a(n-3) -2*a(n-4) -3*a(n-5) +2*a(n-6) for n>8

k=6: [order 11] for n>12

k=7: [order 14] for n>17

Empirical for row n:

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

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

n=3: a(n) = 2*a(n-1) -a(n-4) for n>6

n=4: a(n) = 2*a(n-1) +a(n-3) -a(n-4) -2*a(n-6) +a(n-7) for n>9

n=5: [order 14] for n>17

n=6: [order 27] for n>32

n=7: [order 47] for n>52

Example

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A001519(n+1).

Row 1 is A000045(n+1).

Row 2 is A301791.

Sequence in context: A209762 A026408 A301790 * A334043 A301884 A302081

Adjacent sequences: A301961 A301962 A301963 * A301965 A301966 A301967

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 29 2018

Status

approved