A303197 - OEIS

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A303197

T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3, 5 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

1, 2, 2, 3, 3, 4, 5, 9, 6, 8, 8, 17, 12, 10, 16, 13, 25, 23, 23, 21, 32, 21, 65, 43, 46, 62, 42, 64, 34, 185, 105, 97, 185, 122, 86, 128, 55, 385, 233, 283, 523, 497, 305, 179, 256, 89, 649, 479, 687, 2106, 1751, 1357, 793, 370, 512, 144, 1489, 968, 1642, 7425, 8250, 5573

(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....9....17....25.....65.....185......385.......649.......1489

...4...6...12....23....43....105.....233......479.......968.......2146

...8..10...23....46....97....283.....687.....1642......3949......10169

..16..21...62...185...523...2106....7425....23976.....77199.....278516

..32..42..122...497..1751...8250...34801...138014....547379....2363422

..64..86..305..1357..5573..32223..164295...791150...3806973...20061588

.128.179..793..4207.21575.159440.1053249..6303961..38494616..258640170

.256.370.1757.12167.76833.703465.5803057.43287208.332058205.2785202370

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..241

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 7] for n>11

k=4: [order 42] for n>43

k=5: [order 33] for n>37

Empirical for row n:

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

n=2: a(n) = a(n-1) +16*a(n-4) -8*a(n-5) for n>6

n=3: [order 18] for n>19

n=4: [order 70] for n>71

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

CROSSREFS

Column 1 is A000079(n-1).

Column 2 is A240513.

Row 1 is A000045(n+1).

Row 2 is A302164.

Sequence in context: A302163 A302635 A302427 * A059185 A302309 A303040

Adjacent sequences: A303194 A303195 A303196 * A303198 A303199 A303200

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Apr 19 2018

STATUS

approved