A183907 Number of nondecreasing arrangements of n+2 numbers in 0..4 with each number being the sum mod 5 of two others.

1, 2, 20, 66, 148, 275, 457, 705, 1031, 1448, 1970, 2612, 3390, 4321, 5423, 6715, 8217, 9950, 11936, 14198, 16760, 19647, 22885, 26501, 30523, 34980, 39902, 45320, 51266, 57773, 64875, 72607, 81005, 90106, 99948, 110570, 122012, 134315, 147521, 161673

Offset

1,2

Comments

Column 4 of A183912.

Links

R. H. Hardin, Table of n, a(n) for n = 1..180

Formula

Empirical: a(n) = (1/24)*n^4 + (3/4)*n^3 + (119/24)*n^2 - (95/4)*n + 23 for n>1.

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

G.f.: x*(1 - 3*x + 20*x^2 - 24*x^3 + 3*x^4 + 4*x^5) / (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>6.

(End)

Example

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

Crossrefs

Cf. A183912.

Sequence in context: A192351 A136905 A230644 * A216609 A226394 A287485

Adjacent sequences: A183904 A183905 A183906 * A183908 A183909 A183910

Keyword

nonn

Author

R. H. Hardin, Jan 07 2011

Status

approved