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Search: a241130 -id:a241130
Displaying 1-5 of 5 results found. page 1
     Sort: relevance | references | number | modified | created      Format: long | short | data
A241125 Number of n X 2 0..2 arrays with no element equal to exactly two horizontal and vertical neighbors, with new values 0..2 introduced in row major order. +10
1
2, 9, 54, 325, 1965, 11876, 71793, 434007, 2623694, 15861001, 95884409, 579649484, 3504151829, 21183629803, 128061281038, 774168159805, 4680074530261, 28292428888436, 171036065180937, 1033963386740399, 6250613190784174 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
FORMULA
Empirical: a(n) = 6*a(n-1) + 2*a(n-2) - 9*a(n-3) - 10*a(n-4) + 8*a(n-5) for n>6.
Empirical g.f.: x*(1 - x)*(1 - 2*x)*(2 + 3*x + x^2 - 2*x^3) / (1 - 6*x - 2*x^2 + 9*x^3 + 10*x^4 - 8*x^5). - Colin Barker, Oct 29 2018
EXAMPLE
Some solutions for n=4:
..0..1....0..1....0..0....0..1....0..1....0..1....0..1....0..1....0..0....0..1
..1..2....0..1....1..2....2..0....0..2....1..0....1..0....1..2....1..2....0..1
..2..0....1..2....0..1....0..1....1..1....0..1....1..2....1..0....0..2....1..0
..1..1....2..0....1..2....0..1....2..2....0..2....2..0....0..1....0..1....1..0
CROSSREFS
Column 2 of A241130.
KEYWORD
nonn
AUTHOR
R. H. Hardin, Apr 16 2014
STATUS
approved
A241126 Number of nX3 0..2 arrays with no element equal to exactly two horizontal and vertical neighbors, with new values 0..2 introduced in row major order +10
1
4, 54, 723, 9773, 132369, 1792237, 24269723, 328645291, 4450319537, 60263615333, 816054461063, 11050530322615, 149639792084929, 2026334190350265, 27439427668181531, 371568616043522567, 5031563999805819365 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Column 3 of A241130
LINKS
FORMULA
Empirical: a(n) = 14*a(n-1) -7*a(n-2) +27*a(n-3) -170*a(n-4) -631*a(n-5) -1135*a(n-6) +5278*a(n-7) -3113*a(n-8) +5125*a(n-9) +13678*a(n-10) -10325*a(n-11) +15744*a(n-12) -52520*a(n-13) -13756*a(n-14) -110176*a(n-15) +64424*a(n-16) -53672*a(n-17) -13552*a(n-18) +87456*a(n-19) -198528*a(n-20) +71552*a(n-21) -44288*a(n-22) -116224*a(n-23) -4096*a(n-24) -122880*a(n-25) -65536*a(n-26)
EXAMPLE
Some solutions for n=4
..0..1..1....0..1..1....0..1..0....0..1..0....0..1..2....0..1..0....0..1..0
..1..0..0....2..0..2....2..0..1....1..0..2....0..2..1....0..2..1....1..2..0
..0..2..1....1..0..2....1..0..1....0..1..0....1..0..2....1..2..1....0..1..1
..1..2..0....2..1..1....2..1..0....2..1..2....2..0..1....0..1..2....1..2..0
KEYWORD
nonn
AUTHOR
R. H. Hardin, Apr 16 2014
STATUS
approved
A241127 Number of nX4 0..2 arrays with no element equal to exactly two horizontal and vertical neighbors, with new values 0..2 introduced in row major order +10
1
11, 325, 9773, 295584, 8974020, 272418756, 8270609664, 251096788713, 7623351508315, 231446775293031, 7026779711400192, 213334731852107120, 6476894113062087316, 196640073775126182008, 5970040263453594766199 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Column 4 of A241130
LINKS
EXAMPLE
Some solutions for n=3
..0..1..2..0....0..1..2..0....0..1..0..1....0..0..1..0....0..0..0..1
..2..1..2..0....2..1..0..2....2..1..1..2....1..1..2..1....2..0..2..0
..1..2..0..1....0..2..2..1....0..1..0..1....2..0..0..2....0..2..1..1
KEYWORD
nonn
AUTHOR
R. H. Hardin, Apr 16 2014
STATUS
approved
A241128 Number of nX5 0..2 arrays with no element equal to exactly two horizontal and vertical neighbors, with new values 0..2 introduced in row major order +10
1
30, 1965, 132369, 8974020, 611547441, 41661463219, 2838552905280, 193403197619803, 13177423185201303, 897837461485635262, 61173728850055840649, 4168043075184317942781, 283987643903962340437622 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Column 5 of A241130
LINKS
EXAMPLE
Some solutions for n=3
..0..1..2..0..1....0..0..1..2..0....0..1..0..1..0....0..1..2..1..1
..2..1..0..2..2....2..1..0..1..2....2..2..0..0..2....1..0..2..0..0
..0..2..2..1..0....0..1..2..1..0....1..1..0..1..0....0..0..0..2..2
KEYWORD
nonn
AUTHOR
R. H. Hardin, Apr 16 2014
STATUS
approved
A241129 Number of nX6 0..2 arrays with no element equal to exactly two horizontal and vertical neighbors, with new values 0..2 introduced in row major order +10
1
82, 11876, 1792237, 272418756, 41661463219, 6369134821236, 973866422990563, 148910067386335603, 22769250775360645781, 3481561098182183872590, 532352524971939702558325, 81400042312275755768027497 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Column 6 of A241130
LINKS
EXAMPLE
Some solutions for n=2
..0..1..1..1..2..1....0..1..0..2..0..2....0..1..0..1..0..1....0..1..2..1..2..1
..0..2..1..0..1..0....1..0..2..0..0..0....1..0..0..0..1..2....2..2..0..0..2..0
KEYWORD
nonn
AUTHOR
R. H. Hardin, Apr 16 2014
STATUS
approved
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Last modified August 30 07:09 EDT 2024. Contains 375532 sequences. (Running on oeis4.)