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A302309 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3 or 4 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero. 13
1, 2, 2, 3, 3, 4, 5, 11, 6, 8, 8, 21, 13, 10, 16, 13, 31, 26, 33, 21, 32, 21, 113, 48, 66, 58, 42, 64, 34, 363, 121, 194, 153, 153, 86, 128, 55, 813, 275, 663, 445, 380, 336, 179, 256, 89, 1751, 600, 2048, 1595, 1271, 1090, 937, 370, 512, 144, 5001, 1296, 5790, 4772, 5715 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Table starts

...1...2....3....5.....8.....13......21.......34........55.........89

...2...3...11...21....31....113.....363......813......1751.......5001

...4...6...13...26....48....121.....275......600......1296.......2998

...8..10...33...66...194....663....2048.....5790.....17761......58980

..16..21...58..153...445...1595....4772....15249.....49634.....166329

..32..42..153..380..1271...5715...18992....70289....276303....1198933

..64..86..336.1090..3915..18990...76642...360898...1695748....9408402

.128.179..937.3120.12420..73663..364922..2150420..13123505...95790405

.256.370.2449.9130.42897.312122.1991487.15392485.124691962.1235540899

LINKS

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

FORMULA

Empirical for column k:

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

k=2: a(n) = 2*a(n-1) +a(n-2) -a(n-3) -2*a(n-4) +a(n-5)

k=3: [order 13] for n>16

k=4: [order 60] for n>61

Empirical for row n:

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

n=2: a(n) = 2*a(n-1) -a(n-2) +4*a(n-3) +12*a(n-4) -16*a(n-5) for n>6

n=3: [order 15] for n>16

n=4: [order 61] for n>64

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

CROSSREFS

Column 1 is A000079(n-1).

Column 2 is A240513.

Row 1 is A000045(n+1).

Sequence in context: A302427 A303197 A059185 * A303040 A302877 A303525

Adjacent sequences:  A302306 A302307 A302308 * A302310 A302311 A302312

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Apr 05 2018

STATUS

approved

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Last modified January 27 09:09 EST 2020. Contains 331293 sequences. (Running on oeis4.)