A269621 Number of length-5 0..n arrays with no repeated value differing from the previous repeated value by other than plus two, zero or minus 1.

28, 222, 954, 2956, 7440, 16218, 31822, 57624, 97956, 158230, 245058, 366372, 531544, 751506, 1038870, 1408048, 1875372, 2459214, 3180106, 4060860, 5126688, 6405322, 7927134, 9725256, 11835700, 14297478, 17152722, 20446804, 24228456

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 + 3*n.

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

G.f.: 2*x*(14 + 27*x + 21*x^2 + x^3 - 3*x^4) / (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=8:
..5. .0. .5. .4. .4. .7. .7. .8. .0. .1. .1. .3. .6. .0. .2. .3
..4. .1. .0. .6. .8. .8. .6. .3. .8. .5. .5. .8. .5. .4. .0. .5
..5. .2. .7. .5. .3. .0. .0. .4. .6. .3. .6. .0. .7. .5. .4. .4
..5. .0. .7. .6. .2. .6. .4. .0. .7. .0. .8. .1. .2. .0. .2. .4
..7. .1. .4. .6. .1. .6. .5. .8. .7. .6. .1. .2. .7. .4. .3. .5

Crossrefs

Row 5 of A269619.

Sequence in context: A340908 A297614 A249710 * A269437 A236355 A133071

Adjacent sequences: A269618 A269619 A269620 * A269622 A269623 A269624

Keyword

nonn

Author

R. H. Hardin, Mar 01 2016

Status

approved