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A305340 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 5 or 8 king-move adjacent elements, with upper left element zero. 7
1, 2, 2, 4, 4, 4, 8, 5, 5, 8, 16, 9, 12, 9, 16, 32, 22, 26, 26, 22, 32, 64, 45, 62, 81, 62, 45, 64, 128, 101, 166, 267, 267, 166, 101, 128, 256, 218, 431, 938, 1185, 938, 431, 218, 256, 512, 477, 1091, 3186, 5296, 5296, 3186, 1091, 477, 512, 1024, 1041, 2812, 10840 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Table starts

...1...2....4.....8.....16......32.......64.......128.........256..........512

...2...4....5.....9.....22......45......101.......218.........477.........1041

...4...5...12....26.....62.....166......431......1091........2812.........7268

...8...9...26....81....267.....938.....3186.....10840.......37115.......127093

..16..22...62...267...1185....5296....23348....103641......460756......2046399

..32..45..166...938...5296...30826...176673...1020555.....5903993.....34127533

..64.101..431..3186..23348..176673..1321695...9959836....75112075....566241938

.128.218.1091.10840.103641.1020555..9959836..98008416...964336401...9486731570

.256.477.2812.37115.460756.5903993.75112075.964336401.12373093291.158745150050

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..391

FORMULA

Empirical for column k:

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

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

k=3: a(n) = a(n-1) +3*a(n-2) +3*a(n-3) +2*a(n-4) -3*a(n-5) -8*a(n-6) -4*a(n-7) for n>8

k=4: [order 15] for n>19

k=5: [order 32] for n>34

k=6: [order 62] for n>66

EXAMPLE

Some solutions for n=5 k=4

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

..0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..0

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

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

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

CROSSREFS

Column 1 is A000079(n-1).

Column 2 is A052962 for n>2.

Sequence in context: A230014 A319414 A303961 * A304604 A316420 A304926

Adjacent sequences:  A305337 A305338 A305339 * A305341 A305342 A305343

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, May 30 2018

STATUS

approved

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Last modified December 5 15:06 EST 2021. Contains 349557 sequences. (Running on oeis4.)