A299839 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3, 4, 5, 6 or 8 king-move adjacent elements, with upper left element zero.

0, 1, 1, 1, 4, 1, 2, 18, 18, 2, 3, 64, 142, 64, 3, 5, 236, 1000, 1000, 236, 5, 8, 888, 7388, 13850, 7388, 888, 8, 13, 3336, 54611, 198202, 198202, 54611, 3336, 13, 21, 12512, 402928, 2853873, 5544044, 2853873, 402928, 12512, 21, 34, 46928, 2973312

Offset

1,5

Comments

Table starts

..0.....1........1..........2.............3................5..................8

..1.....4.......18.........64...........236..............888...............3336

..1....18......142.......1000..........7388............54611.............402928

..2....64.....1000......13850........198202..........2853873...........41026724

..3...236.....7388.....198202.......5544044........156175241.........4390323230

..5...888....54611....2853873.....156175241.......8606994457.......473261273932

..8..3336...402928...41026724....4390323230.....473261273932.....50892107038125

.13.12512..2973312..589665345..123389988671...26017342950926...5471622342472717

.21.46928.21942164.8475712818.3468206088400.1430440832008036.588340577558059509

Links

R. H. Hardin, Table of n, a(n) for n = 1..199

Formula

Empirical for column k:

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

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

k=3: [order 9] for n>10

k=4: [order 22] for n>23

k=5: [order 68] for n>69

Example

Some solutions for n=5 k=4
..0..0..1..0. .0..0..1..0. .0..0..0..0. .0..0..0..0. .0..0..0..1
..0..1..1..0. .0..0..1..0. .1..1..0..0. .0..1..1..0. .0..0..0..1
..0..1..0..1. .1..1..1..1. .0..0..0..1. .1..0..0..0. .0..0..0..1
..0..0..0..1. .0..0..0..0. .0..1..1..1. .0..1..0..0. .1..0..1..1
..1..1..1..1. .1..1..0..0. .1..0..0..1. .1..1..1..1. .1..0..1..1

Crossrefs

Column 1 is A000045(n-1).

Column 2 is A231950(n-1).

Sequence in context: A299937 A299067 A299728 * A265178 A159766 A280284

Adjacent sequences: A299836 A299837 A299838 * A299840 A299841 A299842

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 20 2018

Status

approved