A266131 T(n,k) = Number of n X k integer arrays with each element equal to the number of horizontal, diagonal and antidiagonal neighbors exactly one smaller than itself.

1, 3, 1, 4, 9, 1, 5, 25, 20, 1, 9, 49, 77, 61, 1, 16, 149, 117, 385, 189, 1, 25, 625, 278, 572, 2099, 544, 1, 39, 2141, 1959, 3851, 4336, 9083, 1629, 1, 64, 5433, 11044, 44623, 62104, 19750, 48188, 4973, 1, 105, 17269, 36730, 347576, 1285961, 326145, 102201, 249446

Offset

1,2

Comments

Table starts

.1.....3.......4........5.........9.........16..........25.........39

.1.....9......25.......49.......149........625........2141.......5433

.1....20......77......117.......278.......1959.......11044......36730

.1....61.....385......572......3851......44623......347576....1650710

.1...189....2099.....4336.....62104....1285961....16386099..124675418

.1...544....9083....19750....326145...13689944...325554385.3901509248

.1..1629...48188...102201...4176690..311260836.10444421518

.1..4973..249446...620508..50677045.6688962679

.1.15040.1166325..3041449.367191341

.1.45739.6288299.16217839

Links

R. H. Hardin, Table of n, a(n) for n = 1..97

Formula

Empirical for column k:

k=1: a(n) = a(n-1),

k=2: [order 10],

k=3: [order 26] for n>27,

Empirical for row n:

n=1: a(n) = a(n-1) +a(n-3) +a(n-4),

n=2: [order 17],

n=3: [order 77].

Example

Some solutions for n=4, k=4
..0..0..1..1....0..2..1..2....1..0..2..1....2..1..2..0....0..2..1..0
..0..2..0..1....0..0..1..2....0..2..0..1....0..1..2..0....0..2..1..1
..0..0..1..2....0..2..0..2....3..2..1..1....1..0..2..0....0..2..0..2
..0..2..1..2....0..0..1..1....0..2..1..0....1..1..0..0....0..0..1..1

Crossrefs

Column 2 is A196212.

Row 1 is A195971.

Sequence in context: A049916 A220605 A094166 * A338871 A202353 A108621

Adjacent sequences: A266128 A266129 A266130 * A266132 A266133 A266134

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 21 2015

Status

approved