A265993 Number of 3 X n integer arrays with each element equal to the number of horizontal and antidiagonal neighbors not equal to itself.

1, 2, 6, 2, 3, 9, 9, 16, 27, 35, 55, 105, 145, 202, 369, 589, 857, 1371, 2229, 3444, 5411, 8585, 13399, 21170, 33573, 52488, 82413, 130606, 205585, 322481, 508515, 801862, 1261277, 1985864, 3128187, 4924251, 7755005, 12214150, 19226531, 30273410

Offset

1,2

Links

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

Formula

Empirical: a(n) = a(n-1) + 2*a(n-3) + a(n-4) - 3*a(n-5) - a(n-6) - a(n-7) + a(n-8) + 7*a(n-9) - 2*a(n-10) - 4*a(n-11) + 9*a(n-14) + 3*a(n-15) - 8*a(n-16) - 4*a(n-17) for n>20.

Empirical g.f.: x*(1 + x + 4*x^2 - 6*x^3 - 4*x^4 - 5*x^5 - 3*x^6 + 20*x^7 + 3*x^8 - 11*x^9 - 7*x^10 - 17*x^11 + 12*x^12 + 16*x^13 - 17*x^14 - 18*x^15 - 13*x^16 - 3*x^17 + 8*x^18 + 4*x^19) / ((1 - x)*(1 + x^2 - x^3 - x^4 + 3*x^7 + 2*x^8)*(1 - x^2 - x^3 - x^4 - 3*x^7 - 2*x^8)). - Colin Barker, Jan 09 2019

Example

Some solutions for n=6:
..1..3..1..1..3..2....1..3..2..2..3..1....1..3..1..1..1..2....1..3..1..1..3..2
..1..1..1..1..1..1....2..3..3..4..1..1....1..1..4..1..1..1....2..1..1..1..1..1
..2..3..1..1..3..1....1..1..1..1..3..1....1..3..1..1..3..1....1..3..1..1..3..1

Crossrefs

Row 3 of A265991.

Sequence in context: A316259 A057892 A334188 * A115009 A151944 A073094

Adjacent sequences: A265990 A265991 A265992 * A265994 A265995 A265996

Keyword

nonn

Author

R. H. Hardin, Dec 19 2015

Status

approved