A265991 T(n,k)=Number of nXk integer arrays with each element equal to the number of horizontal and antidiagonal neighbors not equal to itself.

1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 2, 6, 1, 1, 2, 4, 2, 10, 1, 1, 1, 6, 3, 2, 30, 2, 1, 1, 7, 9, 2, 7, 66, 1, 1, 2, 11, 9, 4, 1, 7, 182, 1, 1, 1, 15, 16, 24, 26, 1, 21, 442, 2, 1, 1, 26, 27, 15, 59, 5, 1, 35, 1166, 1, 1, 2, 48, 35, 47, 45, 137, 101, 1, 78, 2930, 1, 1, 1, 82, 55, 68, 64, 82, 422, 17

Offset

1,4

Comments

Table starts

.1.1....2...1.1...2....1...1....2....1.....1.....2.....1.....1......2......1

.1.1....2...2.4...6....7..11...15...26....48....82...135...227....375....634

.1.2....6...2.3...9....9..16...27...35....55...105...145...202....369....589

.1.1...10...2.2...4...24..15...47...68...112...196...281...672...1284...2333

.1.1...30...7.1..26...59..45...64..186...295...506...885..1725...3265...5893

.1.2...66...7.1...5..137..82..118..178...354...853..1574..3143...6240..11295

.1.1..182..21.1.101..422.182..157..705..1843..2314..4008.10135..19799..33914

.1.1..442..35.1..17..865.243..282..550..3174..4849..8659.19176..36130..78174

.1.2.1166..78.1.401.2777.771..299.2206.12817.15240.29210.49647.139162.285423

.1.1.2930.158.1..65.5666.975.1010.1712.26825.24453.35505.79080.381291.788692

Links

R. H. Hardin, Table of n, a(n) for n = 1..447

Formula

Empirical for column k:

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

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

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

k=4: a(n) = a(n-1) +2*a(n-2) +a(n-3) -a(n-5) -3*a(n-6) +a(n-7)

k=5: a(n) = a(n-1) for n>5

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

k=7: [order 10] for n>15

Empirical for row n:

n=1: a(n) = a(n-3)

n=2: [order 11] for n>14

n=3: [order 17] for n>20

n=4: [order 70] for n>75

Example

All solutions for n=4 k=4
..0..0..0..0....1..3..1..1
..0..0..0..0....1..1..3..1
..0..0..0..0....1..3..1..1
..0..0..0..0....1..1..3..1

Crossrefs

Sequence in context: A334440 A316975 A043277 * A353841 A322871 A322870

Adjacent sequences: A265988 A265989 A265990 * A265992 A265993 A265994

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 19 2015

Status

approved