A205408 Number of (n+2) X 3 0..2 arrays with every 3 X 3 subblock having three equal elements in a row horizontally, vertically or nw-to-se diagonally exactly two ways, and new values 0..2 introduced in row major order.

468, 3868, 33322, 236576, 1820215, 14452683, 109757792, 844627201, 6555663807, 50395116296, 388310279461, 2998496455277, 23106198583152, 178125506630869, 1373888878002903, 10592170949339668, 81666691848271821, 629737361145882421

Offset

1,1

Comments

Column 1 of A205415.

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = 3*a(n-1) +15*a(n-2) +210*a(n-3) -46*a(n-4) -1180*a(n-5) -8860*a(n-6) -9460*a(n-7) +35477*a(n-8) +165003*a(n-9) +271917*a(n-10) -292806*a(n-11) -1718502*a(n-12) -2698834*a(n-13) -1465296*a(n-14) +4872048*a(n-15) +13801984*a(n-16) +30802224*a(n-17) +54371712*a(n-18) +14213752*a(n-19) -115878688*a(n-20) -314261840*a(n-21) -579542448*a(n-22) -599435264*a(n-23) +450034176*a(n-24) +2993109568*a(n-25) +6140523968*a(n-26) +5188675584*a(n-27) -5040264704*a(n-28) -21090059008*a(n-29) -30058399232*a(n-30) -12075326464*a(n-31) +39301468160*a(n-32) +79235510272*a(n-33) +29768392704*a(n-34) -75591352320*a(n-35) -84606517248*a(n-36) +10132783104*a(n-37) +59464876032*a(n-38) +26931363840*a(n-39).

Example

Some solutions for n=3
..0..0..0....0..0..0....0..0..1....0..0..1....0..0..0....0..0..0....0..1..2
..1..1..2....0..1..2....2..0..1....1..1..1....0..0..0....1..0..2....0..2..2
..0..0..0....0..1..2....1..0..0....0..1..1....1..1..2....0..1..0....0..1..2
..2..2..2....0..2..2....0..0..0....0..0..0....2..2..2....1..1..1....0..1..2
..1..2..1....0..2..2....2..1..0....0..2..2....2..0..2....0..0..0....1..1..1

Crossrefs

Cf. A205415.

Sequence in context: A043364 A054756 A205415 * A282116 A281061 A270259

Adjacent sequences: A205405 A205406 A205407 * A205409 A205410 A205411

Keyword

nonn

Author

R. H. Hardin, Jan 26 2012

Status

approved