A269641 Number of length-4 0..n arrays with no repeated value differing from the previous repeated value by other than plus two or minus 1.

9, 63, 221, 567, 1209, 2279, 3933, 6351, 9737, 14319, 20349, 28103, 37881, 50007, 64829, 82719, 104073, 129311, 158877, 193239, 232889, 278343, 330141, 388847, 455049, 529359, 612413, 704871, 807417, 920759, 1045629, 1182783, 1333001

Offset

1,1

Links

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

Formula

Empirical: a(n) = n^4 + 4*n^3 + 3*n^2 + 2*n - 1.

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

G.f.: x*(3 - x)*(3 + 7*x + x^2 + x^3) / (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>5.

(End)

Example

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

Crossrefs

Row 4 of A269640.

Sequence in context: A085645 A299579 A344526 * A269410 A379683 A178161

Adjacent sequences: A269638 A269639 A269640 * A269642 A269643 A269644

Keyword

nonn

Author

R. H. Hardin, Mar 02 2016

Status

approved