A304959 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 3, 5 or 7 king-move adjacent elements, with upper left element zero.

0, 1, 1, 1, 7, 1, 2, 16, 16, 2, 3, 45, 42, 45, 3, 5, 120, 118, 118, 120, 5, 8, 333, 371, 496, 371, 333, 8, 13, 928, 1203, 2080, 2080, 1203, 928, 13, 21, 2613, 3917, 8361, 11282, 8361, 3917, 2613, 21, 34, 7400, 12919, 35441, 60568, 60568, 35441, 12919, 7400, 34

Offset

1,5

Comments

Table starts

..0....1.....1......2........3.........5..........8..........13...........21

..1....7....16.....45......120.......333........928........2613.........7400

..1...16....42....118......371......1203.......3917.......12919........42060

..2...45...118....496.....2080......8361......35441......148491.......621640

..3..120...371...2080....11282.....60568.....334906.....1852576.....10208628

..5..333..1203...8361....60568....435964....3174054....23304518....170481467

..8..928..3917..35441...334906...3174054...30361694...294236689...2849022835

.13.2613.12919.148491..1852576..23304518..294236689..3805684538..49133027076

.21.7400.42060.621640.10208628.170481467.2849022835.49133027076.844100991906

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) +5*a(n-2) -2*a(n-3) -12*a(n-4) -8*a(n-5) for n>6

k=3: [order 20] for n>21

k=4: [order 69] for n>71

Example

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

Crossrefs

Column 1 is A000045(n-1).

Column 2 is A304013.

Sequence in context: A316740 A304019 A305367 * A316641 A304697 A316448

Adjacent sequences: A304956 A304957 A304958 * A304960 A304961 A304962

Keyword

nonn,tabl

Author

R. H. Hardin, May 22 2018

Status

approved