A183900 Number of nondecreasing arrangements of n+3 numbers in 0..5 with each number being the sum mod 6 of three others.

3, 24, 130, 364, 771, 1386, 2281, 3534, 5236, 7492, 10422, 14162, 18865, 24702, 31863, 40558, 51018, 63496, 78268, 95634, 115919, 139474, 166677, 197934, 233680, 274380, 320530, 372658, 431325, 497126, 570691, 652686, 743814, 844816, 956472, 1079602

Offset

1,1

Comments

Column 5 of A183904.

Links

R. H. Hardin, Table of n, a(n) for n = 1..57

Formula

Empirical: a(n) = (1/120)*n^5 + (1/4)*n^4 + (71/24)*n^3 + (57/4)*n^2 - (262/15)*n - 50 for n>4.

Conjectures from Colin Barker, Apr 05 2018: (Start)

G.f.: x*(3 + 6*x + 31*x^2 - 116*x^3 + 102*x^4 - 38*x^5 + 59*x^6 - 78*x^7 + 38*x^8 - 6*x^9) / (1 - x)^6.

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>10.

(End)

Example

Some solutions for n=2:
..0....1....0....0....0....0....0....0....0....0....0....3....1....3....0....1
..2....3....0....1....0....0....0....1....2....1....0....3....3....3....2....1
..4....5....2....3....2....2....0....1....4....2....4....5....3....3....2....1
..4....5....4....4....2....2....0....2....5....3....4....5....5....3....2....3
..4....5....4....5....4....2....0....4....5....4....4....5....5....3....4....3

Crossrefs

Cf. A183904.

Sequence in context: A326789 A305543 A356363 * A001089 A359884 A069515

Adjacent sequences: A183897 A183898 A183899 * A183901 A183902 A183903

Keyword

nonn

Author

R. H. Hardin, Jan 07 2011

Status

approved