A269642 Number of length-5 0..n arrays with no repeated value differing from the previous repeated value by other than plus two or minus 1.

12, 159, 796, 2637, 6876, 15307, 30444, 55641, 95212, 154551, 240252, 360229, 523836, 741987, 1027276, 1394097, 1858764, 2439631, 3157212, 4034301, 5096092, 6370299, 7887276, 9680137, 11784876, 14240487, 17089084, 20376021, 24150012

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 - 5*n + 1.

Conjectures from Colin Barker, Jan 25 2019: (Start)

G.f.: x*(12 + 87*x + 22*x^2 + 6*x^3 - 6*x^4 - x^5) / (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. .0. .0. .1. .1. .2. .0. .2. .0. .2. .1. .0. .3. .2. .0. .3
..3. .0. .0. .0. .2. .3. .1. .3. .1. .2. .1. .3. .2. .0. .2. .0
..1. .1. .1. .2. .2. .2. .2. .0. .3. .3. .0. .0. .0. .1. .0. .0
..0. .3. .2. .3. .1. .3. .3. .1. .1. .2. .0. .3. .3. .0. .0. .1
..3. .1. .2. .3. .0. .1. .1. .2. .2. .3. .2. .0. .0. .0. .1. .2

Crossrefs

Row 5 of A269640.

Sequence in context: A015000 A220225 A213376 * A269411 A347748 A226297

Adjacent sequences: A269639 A269640 A269641 * A269643 A269644 A269645

Keyword

nonn

Author

R. H. Hardin, Mar 02 2016

Status

approved