Search: a241130 -id:a241130
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A241125
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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.
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+10
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2, 9, 54, 325, 1965, 11876, 71793, 434007, 2623694, 15861001, 95884409, 579649484, 3504151829, 21183629803, 128061281038, 774168159805, 4680074530261, 28292428888436, 171036065180937, 1033963386740399, 6250613190784174
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OFFSET
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1,1
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LINKS
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FORMULA
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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
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EXAMPLE
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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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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A241126
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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
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+10
1
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4, 54, 723, 9773, 132369, 1792237, 24269723, 328645291, 4450319537, 60263615333, 816054461063, 11050530322615, 149639792084929, 2026334190350265, 27439427668181531, 371568616043522567, 5031563999805819365
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OFFSET
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1,1
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COMMENTS
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LINKS
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FORMULA
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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)
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EXAMPLE
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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
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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A241127
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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
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+10
1
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11, 325, 9773, 295584, 8974020, 272418756, 8270609664, 251096788713, 7623351508315, 231446775293031, 7026779711400192, 213334731852107120, 6476894113062087316, 196640073775126182008, 5970040263453594766199
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OFFSET
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1,1
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COMMENTS
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LINKS
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EXAMPLE
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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
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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A241128
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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
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+10
1
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30, 1965, 132369, 8974020, 611547441, 41661463219, 2838552905280, 193403197619803, 13177423185201303, 897837461485635262, 61173728850055840649, 4168043075184317942781, 283987643903962340437622
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graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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LINKS
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EXAMPLE
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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
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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A241129
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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
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+10
1
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82, 11876, 1792237, 272418756, 41661463219, 6369134821236, 973866422990563, 148910067386335603, 22769250775360645781, 3481561098182183872590, 532352524971939702558325, 81400042312275755768027497
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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LINKS
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EXAMPLE
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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
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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