A269585 Number of length-5 0..n arrays with no repeated value differing from the previous repeated value by more than one.

32, 229, 964, 2969, 7456, 16237, 31844, 57649, 97984, 158261, 245092, 366409, 531584, 751549, 1038916, 1408097, 1875424, 2459269, 3180164, 4060921, 5126752, 6405389, 7927204, 9725329, 11835776, 14297557, 17152804, 20446889, 24228544

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 + 12*n^2 + 6*n + 1.

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

G.f.: x*(32 + 37*x + 70*x^2 - 20*x^3 + 2*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).

(End)

Example

Some solutions for n=6:
..5. .4. .1. .6. .2. .4. .0. .4. .6. .6. .3. .6. .2. .1. .1. .0
..3. .2. .5. .6. .1. .0. .6. .5. .5. .2. .4. .3. .6. .1. .4. .4
..5. .4. .4. .0. .5. .1. .5. .1. .4. .4. .0. .2. .6. .2. .3. .6
..2. .2. .2. .2. .4. .2. .6. .6. .4. .5. .3. .1. .1. .2. .6. .5
..2. .0. .6. .0. .4. .4. .4. .1. .2. .6. .3. .0. .2. .6. .0. .4

Crossrefs

Row 5 of A269583.

Sequence in context: A070053 A022146 A160061 * A199913 A301795 A301968

Adjacent sequences: A269582 A269583 A269584 * A269586 A269587 A269588

Keyword

nonn

Author

R. H. Hardin, Mar 01 2016

Status

approved