A183901 Number of nondecreasing arrangements of n+3 numbers in 0..6 with each number being the sum mod 7 of three others.

1, 1, 136, 664, 1720, 3491, 6263, 10400, 16357, 24694, 36091, 51364, 71482, 97585, 131003, 173276, 226175, 291724, 372223, 470272, 588796, 731071, 900751, 1101896, 1339001, 1617026, 1941427, 2318188, 2753854, 3255565, 3831091, 4488868, 5238035

Offset

1,3

Comments

Column 6 of A183904.

Links

R. H. Hardin, Table of n, a(n) for n = 1..37

Formula

Empirical: a(n) = (1/720)*n^6 + (13/240)*n^5 + (125/144)*n^4 + (117/16)*n^3 + (12287/360)*n^2 - (4421/30)*n - 44 for n>3.

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

G.f.: x*(1 - 6*x + 150*x^2 - 302*x^3 - 72*x^4 + 649*x^5 - 548*x^6 + 60*x^7 + 102*x^8 - 33*x^9) / (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>10.

(End)

Example

Some solutions for n=3:
..0....0....3....0....0....0....0....0....0....0....0....1....0....0....2....1
..1....0....3....1....0....0....0....3....2....1....1....1....3....0....4....2
..1....1....3....1....1....3....1....4....3....2....4....2....3....1....4....3
..2....1....4....4....2....3....1....5....4....3....5....3....4....2....5....3
..4....2....4....4....2....5....3....6....4....4....5....4....5....4....5....5
..4....4....4....6....4....6....3....6....6....4....6....5....5....4....6....6

Crossrefs

Cf. A183904.

Sequence in context: A235198 A235191 A076331 * A270341 A234169 A234162

Adjacent sequences: A183898 A183899 A183900 * A183902 A183903 A183904

Keyword

nonn

Author

R. H. Hardin, Jan 07 2011

Status

approved