A269539 Number of length-5 0..n arrays with no repeated value differing from the previous repeated value by other than one.

14, 164, 804, 2648, 6890, 15324, 30464, 55664, 95238, 154580, 240284, 360264, 523874, 742028, 1027320, 1394144, 1858814, 2439684, 3157268, 4034360, 5096154, 6370364, 7887344, 9680208, 11784950, 14240564, 17089164, 20376104, 24150098

Offset

1,1

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = n^5 + 5*n^4 + 4*n^3 + 6*n^2 - 2*n.

Conjectures from Colin Barker, Jan 24 2019: (Start)

G.f.: 2*x*(7 + 40*x + 15*x^2 + 2*x^3 - 4*x^4) / (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>6.

(End)

Example

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

Crossrefs

Row 5 of A269537.

Sequence in context: A238116 A153664 A016146 * A228422 A218089 A273587

Adjacent sequences: A269536 A269537 A269538 * A269540 A269541 A269542

Keyword

nonn

Author

R. H. Hardin, Feb 29 2016

Status

approved