A183899 Number of nondecreasing arrangements of n+3 numbers in 0..4 with each number being the sum mod 5 of three others.

1, 5, 66, 174, 329, 539, 815, 1169, 1614, 2164, 2834, 3640, 4599, 5729, 7049, 8579, 10340, 12354, 14644, 17234, 20149, 23415, 27059, 31109, 35594, 40544, 45990, 51964, 58499, 65629, 73389, 81815, 90944, 100814, 111464, 122934, 135265, 148499, 162679

Offset

1,2

Comments

Column 4 of A183904.

Links

R. H. Hardin, Table of n, a(n) for n = 1..62

Formula

Empirical: a(n) = (1/24)*n^4 + (11/12)*n^3 + (179/24)*n^2 + (199/12)*n - 81 for n>3.

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

G.f.: x*(1 + 51*x^2 - 116*x^3 + 74*x^4 - 2*x^5 - 5*x^6 - 2*x^7) / (1 - x)^5.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>8.

(End)

Example

All solutions for n=2:
..0....0....0....0....0
..1....1....2....1....0
..3....2....3....1....0
..3....2....4....2....0
..4....4....4....3....0

Crossrefs

Cf. A183904.

Sequence in context: A167536 A237887 A042491 * A263784 A263785 A263786

Adjacent sequences: A183896 A183897 A183898 * A183900 A183901 A183902

Keyword

nonn

Author

R. H. Hardin, Jan 07 2011

Status

approved