A316740 T(n,k) = Number of n X k 0..1 arrays with every element unequal to 1, 2, 3, 6, 7 or 8 king-move adjacent elements, with upper left element zero.

0, 1, 1, 1, 7, 1, 2, 14, 14, 2, 3, 33, 23, 33, 3, 5, 70, 36, 36, 70, 5, 8, 157, 210, 95, 210, 157, 8, 13, 346, 509, 410, 410, 509, 346, 13, 21, 769, 1219, 392, 4956, 392, 1219, 769, 21, 34, 1710, 4537, 1124, 25047, 25047, 1124, 4537, 1710, 34, 55, 3813, 12446, 3964, 75856

Offset

1,5

Comments

Table starts

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

..1....7....14...33......70......157.......346.........769.........1710

..1...14....23...36.....210......509......1219........4537........12446

..2...33....36...95.....410......392......1124........3964.........5343

..3...70...210..410....4956....25047.....75856......491644......2699059

..5..157...509..392...25047...144106....625739.....8072260.....60509347

..8..346..1219.1124...75856...625739...1906293....44561267....422993842

.13..769..4537.3964..491644..8072260..44561267..1342645923..23603784309

.21.1710.12446.5343.2699059.60509347.422993842.23603784309.632741511767

Links

R. H. Hardin, Table of n, a(n) for n = 1..220

Formula

Empirical for column k:

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

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

k=3: [order 14] for n > 16;

k=4: [order 19] for n > 24;

k=5: [order 93] for n > 97;

Example

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

Crossrefs

Column 1 is A000045(n-1).

Column 2 is A304143.

Sequence in context: A304149 A305489 A305089 * A304019 A305367 A304959

Adjacent sequences: A316737 A316738 A316739 * A316741 A316742 A316743

Keyword

nonn,tabl

Author

R. H. Hardin, Jul 11 2018

Status

approved