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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. 7
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified December 4 13:06 EST 2021. Contains 349526 sequences. (Running on oeis4.)