A269586 Number of length-6 0..n arrays with no repeated value differing from the previous repeated value by more than one.

64, 659, 3680, 14239, 43184, 110339, 248464, 507935, 962144, 1713619, 2900864, 4705919, 7362640, 11165699, 16480304, 23752639, 33521024, 46427795, 63231904, 84822239, 112231664, 146651779, 189448400, 242177759, 306603424, 384713939

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 + 15*n^2 + 12*n - 1.

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

G.f.: x*(64 + 211*x + 411*x^2 + 78*x^3 - 34*x^4 - 9*x^5 - x^6) / (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>7.

(End)

Example

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

Crossrefs

Row 6 of A269583.

Sequence in context: A136957 A250233 A297666 * A269080 A221509 A283337

Adjacent sequences: A269583 A269584 A269585 * A269587 A269588 A269589

Keyword

nonn

Author

R. H. Hardin, Mar 01 2016

Status

approved