A269680 Number of length-5 0..n arrays with no repeated value differing from the previous repeated value by other than plus or minus one modulo n+1.

14, 174, 820, 2670, 6918, 15358, 30504, 55710, 95290, 154638, 240348, 360334, 523950, 742110, 1027408, 1394238, 1858914, 2439790, 3157380, 4034478, 5096278, 6370494, 7887480, 9680350, 11785098, 14240718, 17089324, 20376270, 24150270

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 + 4*n - 2 for n>1.

Conjectures from Colin Barker, Jan 26 2019: (Start)

G.f.: 2*x*(7 + 45*x - 7*x^2 + 40*x^3 - 36*x^4 + 13*x^5 - 2*x^6) / (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>7.

(End)

Example

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

Crossrefs

Row 5 of A269678.

Sequence in context: A277940 A061484 A097583 * A269469 A349858 A144506

Adjacent sequences: A269677 A269678 A269679 * A269681 A269682 A269683

Keyword

nonn

Author

R. H. Hardin, Mar 03 2016

Status

approved