A299128 - OEIS

A299128

T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3, 4, 5 or 7 king-move adjacent elements, with upper left element zero.

1, 2, 2, 3, 4, 3, 5, 4, 4, 5, 8, 16, 9, 16, 8, 13, 50, 23, 23, 50, 13, 21, 112, 31, 232, 31, 112, 21, 34, 348, 184, 623, 623, 184, 348, 34, 55, 1028, 427, 3368, 2636, 3368, 427, 1028, 55, 89, 2796, 1115, 20226, 13809, 13809, 20226, 1115, 2796, 89, 144, 8216, 4128, 95305

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OFFSET

1,2

COMMENTS

Table starts

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

..2....4....4.....16......50.......112.........348.........1028...........2796

..3....4....9.....23......31.......184.........427.........1115...........4128

..5...16...23....232.....623......3368.......20226........95305.........517446

..8...50...31....623....2636.....13809......132409.......854671........5933446

.13..112..184...3368...13809....198753.....2286535.....21688754......284403950

.21..348..427..20226..132409...2286535....50126162....761448901....14747885320

.34.1028.1115..95305..854671..21688754...761448901..17703574257...537784640291

.55.2796.4128.517446.5933446.284403950.14747885320.537784640291.28274774976231

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 18] for n>19

k=4: [order 66] for n>68

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

CROSSREFS

Column 1 is A000045(n+1).

Column 2 is A298148.

Sequence in context: A300089 A298230 A298154 * A299886 A299052 A299814

Adjacent sequences: A299125 A299126 A299127 * A299129 A299130 A299131

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Feb 03 2018

STATUS

approved