A206858 Number of nX3 0..2 arrays avoiding the pattern z z+1 z in any row, column, diagonal or antidiagonal

25, 625, 11092, 192575, 3425501, 61164640, 1090023439, 19411973287, 345764258689, 6159551322461, 109726321617078, 1954613166621694, 34818594738203574, 620246036769753113, 11048844392776786913

Offset

1,1

Comments

Column 3 of A206863

Links

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

Formula

Empirical: a(n) = 19*a(n-1) -116*a(n-2) +1656*a(n-3) -869*a(n-4) +21477*a(n-5) +132055*a(n-6) -840588*a(n-7) +536035*a(n-8) -6853600*a(n-9) -60451483*a(n-10) +239622640*a(n-11) +438741327*a(n-12) -1195377988*a(n-13) +5700951257*a(n-14) -6858573805*a(n-15) -111005025152*a(n-16) +81130949991*a(n-17) +729595094458*a(n-18) -164145675576*a(n-19) -1939309566165*a(n-20) -923748685709*a(n-21) -1316253867500*a(n-22) +5260520510689*a(n-23) +20022040020338*a(n-24) -5890585307291*a(n-25) -34836595129811*a(n-26) -22702031279219*a(n-27) -33049844533404*a(n-28) +62351641745134*a(n-29) +155113662891657*a(n-30) +33107662721068*a(n-31) -24178641337873*a(n-32) -194402042599881*a(n-33) -311832321249112*a(n-34) -33618123825367*a(n-35) +89850785718241*a(n-36) +300778171884747*a(n-37) +374045469527943*a(n-38) +86092340636653*a(n-39) +3604652678449*a(n-40) -201637013534345*a(n-41) -207248865450281*a(n-42) -71047680122596*a(n-43) -57323557161104*a(n-44) +59400218029312*a(n-45) +25376225539103*a(n-46) +1328368282685*a(n-47) +4014897641042*a(n-48) -31160253752859*a(n-49) +1838520623206*a(n-50) -6407828259429*a(n-51) +3995902092267*a(n-52) +3720821190410*a(n-53) -1212803780265*a(n-54) +697965261753*a(n-55) -2333237925074*a(n-56) -547181285476*a(n-57) -915715203554*a(n-58) -261550523386*a(n-59) -181827672515*a(n-60) -54985098044*a(n-61) -21779928260*a(n-62) -6733838628*a(n-63) -1623288484*a(n-64) -490248576*a(n-65) -68943120*a(n-66) -19647216*a(n-67) -1205568*a(n-68) -323136*a(n-69)

Example

Some solutions for n=4
..0..1..2....2..0..1....0..0..2....2..1..0....2..1..2....2..2..1....2..0..2
..1..2..0....0..0..2....0..0..2....0..1..1....1..2..2....2..0..2....1..1..1
..1..2..0....1..1..2....0..0..0....1..0..2....0..2..1....2..2..0....1..1..0
..2..0..2....1..1..1....1..2..0....1..2..2....1..1..2....0..2..1....1..2..2

Crossrefs

Sequence in context: A208081 A207209 A207203 * A068180 A206952 A206729

Adjacent sequences: A206855 A206856 A206857 * A206859 A206860 A206861

Keyword

nonn

Author

R. H. Hardin Feb 13 2012

Status

approved