A269469 Number of length-5 0..n arrays with no repeated value equal to the previous repeated value.

14, 174, 852, 2780, 7170, 15834, 31304, 56952, 97110, 157190, 243804, 364884, 529802, 749490, 1036560, 1405424, 1872414, 2455902, 3176420, 4056780, 5122194, 6400394, 7921752, 9719400, 11829350, 14290614, 17145324, 20438852, 24219930

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 + 7*n^3 + 2*n^2 - n.

Conjectures from Colin Barker, Jan 23 2019: (Start)

G.f.: 2*x*(7 + 45*x + 9*x^2 - x^3) / (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:
..0. .1. .1. .3. .3. .2. .0. .3. .2. .2. .0. .3. .3. .2. .1. .1
..3. .1. .3. .2. .3. .2. .3. .1. .0. .1. .1. .3. .2. .3. .2. .3
..1. .2. .0. .3. .0. .1. .1. .3. .0. .0. .3. .0. .2. .2. .1. .2
..0. .2. .3. .0. .3. .3. .2. .2. .1. .0. .3. .1. .1. .3. .2. .1
..3. .0. .3. .2. .2. .3. .3. .2. .1. .2. .0. .2. .0. .3. .2. .3

Crossrefs

Row 5 of A269467.

Sequence in context: A061484 A097583 A269680 * A349858 A144506 A177072

Adjacent sequences: A269466 A269467 A269468 * A269470 A269471 A269472

Keyword

nonn

Author

R. H. Hardin, Feb 27 2016

Status

approved