A183898 Number of nondecreasing arrangements of n+3 numbers in 0..3 with each number being the sum mod 4 of three others.

5, 14, 38, 70, 111, 162, 224, 298, 385, 486, 602, 734, 883, 1050, 1236, 1442, 1669, 1918, 2190, 2486, 2807, 3154, 3528, 3930, 4361, 4822, 5314, 5838, 6395, 6986, 7612, 8274, 8973, 9710, 10486, 11302, 12159, 13058, 14000, 14986, 16017, 17094, 18218, 19390

Offset

1,1

Comments

Column 3 of A183904.

Links

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

Formula

Empirical: a(n) = (1/6)*n^3 + (5/2)*n^2 + (25/3)*n - 14 for n>1.

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

G.f.: x*(5 - 6*x + 12*x^2 - 18*x^3 + 8*x^4) / (1 - x)^4.

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

(End)

Example

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

Crossrefs

Cf. A183904.

Sequence in context: A272254 A270452 A270463 * A225865 A319648 A111715

Adjacent sequences: A183895 A183896 A183897 * A183899 A183900 A183901

Keyword

nonn

Author

R. H. Hardin, Jan 07 2011

Status

approved