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A299689 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3, 4, 5, 6 or 7 king-move adjacent elements, with upper left element zero. 7
1, 2, 2, 3, 4, 3, 5, 4, 4, 5, 8, 16, 15, 16, 8, 13, 50, 54, 54, 50, 13, 21, 112, 156, 648, 156, 112, 21, 34, 348, 854, 2850, 2850, 854, 348, 34, 55, 1028, 3226, 20882, 23116, 20882, 3226, 1028, 55, 89, 2796, 13013, 159324, 251922, 251922, 159324, 13013, 2796, 89 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Table starts

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

..2....4.....4......16........50.........112...........348............1028

..3....4....15......54.......156.........854..........3226...........13013

..5...16....54.....648......2850.......20882........159324.........1041908

..8...50...156....2850.....23116......251922.......3247879........36816394

.13..112...854...20882....251922.....5740433.....120453362......2322958629

.21..348..3226..159324...3247879...120453362....4582634341....154482346317

.34.1028.13013.1041908..36816394..2322958629..154482346317...9172624830461

.55.2796.56318.7459468.431156277.49439157520.5662974500151.587385690244582

LINKS

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

FORMULA

Empirical for column k:

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

k=2: a(n) = 2*a(n-1) +2*a(n-2) +6*a(n-3) -10*a(n-4) -8*a(n-5) for n>6

k=3: [order 15] for n>17

k=4: [order 44] for n>46

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

CROSSREFS

Column 1 is A000045(n+1).

Column 2 is A298148.

Sequence in context: A299886 A299052 A299814 * A300321 A026254 A091525

Adjacent sequences:  A299686 A299687 A299688 * A299690 A299691 A299692

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Feb 16 2018

STATUS

approved

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Last modified October 27 23:26 EDT 2020. Contains 338047 sequences. (Running on oeis4.)