A231637 Number of n X 3 0..2 arrays with no element having a strict majority of its horizontal, vertical, diagonal and antidiagonal neighbors equal to itself plus one mod 3, with upper left element zero (rock paper and scissors drawn positions).

3, 25, 362, 5110, 69671, 953726, 13036446, 178192422, 2435768976, 33294651915, 455108952124, 6220940586463, 85034818039884, 1162351701934606, 15888332641640874, 217179633334137617, 2968655946926989630

Offset

1,1

Comments

Column 3 of A231641.

Links

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

Formula

Empirical: a(n) = 21*a(n-1) -107*a(n-2) +63*a(n-3) +327*a(n-4) +1807*a(n-5) -11022*a(n-6) +22286*a(n-7) -29911*a(n-8) +38148*a(n-9) -14430*a(n-10) -114794*a(n-11) +310088*a(n-12) -391497*a(n-13) +122088*a(n-14) +685315*a(n-15) -1613102*a(n-16) +1227640*a(n-17) +817156*a(n-18) -2507835*a(n-19) +2085116*a(n-20) +424904*a(n-21) -3237743*a(n-22) +2923285*a(n-23) -121269*a(n-24) -692469*a(n-25) -329220*a(n-26) +486184*a(n-27) +200957*a(n-28) -63170*a(n-29) -17085*a(n-30) -56817*a(n-31) -12152*a(n-32) +25012*a(n-33) +9826*a(n-34) -5584*a(n-35) -844*a(n-36) +436*a(n-37) +8*a(n-38) for n>39.

Example

Some solutions for n=5
..0..0..1....0..0..0....0..2..1....0..0..0....0..0..0....0..0..1....0..2..1
..1..0..0....1..0..0....1..0..1....0..2..1....0..0..0....0..0..2....2..1..1
..2..0..0....0..0..0....1..0..2....1..1..2....1..2..2....0..1..1....1..2..1
..2..2..1....0..1..2....0..2..2....1..1..1....1..1..2....2..2..1....0..0..0
..0..2..0....2..2..2....0..2..2....2..1..1....2..1..1....2..0..2....1..0..1

Crossrefs

Cf. A231641.

Sequence in context: A161629 A129506 A143139 * A377829 A295765 A012481

Adjacent sequences: A231634 A231635 A231636 * A231638 A231639 A231640

Keyword

nonn

Author

R. H. Hardin, Nov 12 2013

Status

approved