A269622 Number of length-6 0..n arrays with no repeated value differing from the previous repeated value by other than plus two, zero or minus 1.

51, 624, 3611, 14125, 43013, 110099, 248143, 507521, 961625, 1712983, 2900099, 4705013, 7361581, 11164475, 16478903, 23751049, 33519233, 46425791, 63229675, 84819773, 112228949, 146648803, 189445151, 242174225, 306599593, 384709799

Offset

1,1

Links

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

Formula

Empirical: a(n) = n^6 + 6*n^5 + 9*n^4 + 22*n^3 + 9*n^2 + 9*n - 7 for n>2.

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

G.f.: x*(51 + 267*x + 314*x^2 + 167*x^3 - 86*x^4 + 17*x^5 - 14*x^6 + 5*x^7 - x^8) / (1 - x)^7.

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>9.

(End)

Example

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

Crossrefs

Row 6 of A269619.

Sequence in context: A173804 A166820 A269438 * A210055 A020278 A160829

Adjacent sequences: A269619 A269620 A269621 * A269623 A269624 A269625

Keyword

nonn

Author

R. H. Hardin, Mar 01 2016

Status

approved