login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A302515 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 4 or 5 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero. 12
1, 2, 2, 3, 3, 4, 5, 3, 4, 8, 8, 5, 11, 6, 16, 13, 7, 15, 9, 9, 32, 21, 13, 21, 28, 14, 14, 64, 34, 23, 52, 36, 48, 21, 22, 128, 55, 37, 118, 80, 90, 89, 28, 35, 256, 89, 63, 220, 235, 199, 184, 163, 37, 56, 512, 144, 109, 408, 541, 689, 458, 376, 297, 51, 90, 1024, 233, 183 (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......144.......233

...2..3..3...5....7...13....23.....37......63.....109......183.......309

...4..4.11..15...21...52...118....220.....408.....852.....1764......3460

...8..6..9..28...36...80...235....541....1115....2554.....6095.....13920

..16..9.14..48...90..199...689...2125....5410...13908....39850....114503

..32.14.21..89..184..458..1784...7182...22544...67096...220654....775150

..64.22.28.163..376.1088..4558..23944...95681..344525..1302832...5550086

.128.35.37.297..832.2651.12324..82857..414880.1775176..7735877..39371229

.256.56.51.544.1744.6257.32336.282857.1748514.8778929.44362463.272701915

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..511

FORMULA

Empirical for column k:

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

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

k=3: a(n) = a(n-1) +a(n-4) for n>7

k=4: a(n) = a(n-1) +2*a(n-3) +2*a(n-4) -a(n-6) -a(n-7) for n>10

k=5: a(n) = a(n-1) +6*a(n-3) +2*a(n-5) -12*a(n-6) -4*a(n-7) +8*a(n-9) for n>11

k=6: a(n) = a(n-1) +6*a(n-3) +5*a(n-4) +3*a(n-5) -8*a(n-6) -6*a(n-7) -3*a(n-8) for n>12

k=7: [order 15] for n>21

Empirical for row n:

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

n=2: a(n) = a(n-1) +2*a(n-3) for n>5

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

n=4: a(n) = a(n-1) +a(n-2) +3*a(n-3) +5*a(n-4) -a(n-5) -5*a(n-6) -4*a(n-7) for n>10

n=5: [order 13] for n>17

n=6: [order 23] for n>29

n=7: [order 50] for n>55

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

CROSSREFS

Column 1 is A000079(n-1).

Column 2 is A001611(n+1).

Row 1 is A000045(n+1).

Row 2 is A003227(n-1) for n>2.

Sequence in context: A153928 A119446 A302680 * A303314 A076918 A162620

Adjacent sequences:  A302512 A302513 A302514 * A302516 A302517 A302518

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Apr 09 2018

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 20 00:37 EDT 2021. Contains 348098 sequences. (Running on oeis4.)