A298917 - OEIS

A298917

T(n,k) = Number of n X k 0..1 arrays with every element equal to 0, 3, 5, 7 or 8 king-move adjacent elements, with upper left element zero.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 3, 2, 2, 3, 1, 1, 5, 3, 3, 3, 5, 1, 1, 8, 5, 4, 4, 5, 8, 1, 1, 13, 8, 6, 7, 6, 8, 13, 1, 1, 21, 13, 9, 9, 9, 9, 13, 21, 1, 1, 34, 21, 14, 15, 14, 15, 14, 21, 34, 1, 1, 55, 34, 22, 26, 24, 24, 26, 22, 34, 55, 1, 1, 89, 55, 35, 46, 44, 40, 44, 46, 35, 55

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OFFSET

1,12

COMMENTS

Table starts

.1..1..1..1..1..1...1...1...1....1....1.....1.....1......1......1.......1

.1..1..1..2..3..5...8..13..21...34...55....89...144....233....377.....610

.1..2..2..3..4..6...9..14..22...35...56....90...145....234....378.....611

.1..3..3..4..7..9..15..26..46...84..151...276...506....929...1708....3138

.1..5..5..6..9.14..24..44..81..156..306...602..1192...2370...4720....9415

.1..8..8..9.15.24..40..76.141..277..570..1171..2441...5157..10913...23193

.1.13.13.14.26.44..76.168.359..792.1895..4521.10886..26818..66131..163463

.1.21.21.22.46.81.141.359.873.2145.5971.16568.45898.131372.376833.1078872

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..612

FORMULA

Empirical for column k:

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

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

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

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

k=5: a(n) = a(n-1) +a(n-2) +a(n-3) +a(n-5) -a(n-6) -a(n-7) -a(n-8) for n>9.

k=6: a(n) = 3*a(n-1) -2*a(n-2) +a(n-3) -2*a(n-4) -a(n-7) +2*a(n-8) for n>9.

k=7: [order 14] for n>15.

EXAMPLE

All solutions for n=5, k=4

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

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

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

CROSSREFS

Columns 2 and 3 are A000045(n-1).

Column 4 is A001611(n-1).

Sequence in context: A233867 A319814 A220272 * A322530 A303364 A131332

Adjacent sequences: A298914 A298915 A298916 * A298918 A298919 A298920

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Jan 29 2018

STATUS

approved