A238807 Number of n X 3 0..2 arrays with no element equal to one plus the sum of elements to its left or one plus the sum of the sum of elements above it, modulo 3.

4, 15, 48, 118, 254, 498, 916, 1605, 2702, 4395, 6936, 10656, 15982, 23456, 33756, 47719, 66366, 90929, 122880, 163962, 216222, 282046, 364196, 465849, 590638, 742695, 926696, 1147908, 1412238, 1726284, 2097388, 2533691, 3044190, 3638797

Offset

1,1

Links

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

Formula

Empirical: a(n) = (1/360)*n^6 - (1/30)*n^5 + (7/9)*n^4 - (65/12)*n^3 + (11959/360)*n^2 - (1631/20)*n + 83 for n>2.

Conjectures from Colin Barker, Oct 24 2018: (Start)

G.f.: x*(4 - 13*x + 27*x^2 - 43*x^3 + 51*x^4 - 41*x^5 + 27*x^6 - 16*x^7 + 6*x^8) / (1 - x)^7.

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>9.

(End)

Example

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

Crossrefs

Column 3 of A238812.

Sequence in context: A173414 A307075 A219903 * A240333 A227099 A225976

Adjacent sequences: A238804 A238805 A238806 * A238808 A238809 A238810

Keyword

nonn

Author

R. H. Hardin, Mar 05 2014

Status

approved