A269777 Number of length-5 0..n arrays with every repeated value unequal to the previous repeated value plus one mod n+1.

24, 222, 984, 3060, 7680, 16674, 32592, 58824, 99720, 160710, 248424, 370812, 537264, 758730, 1047840, 1419024, 1888632, 2475054, 3198840, 4082820, 5152224, 6434802, 7960944, 9763800, 11879400, 14346774, 17208072, 20508684, 24297360

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 + 10*n^3 + 7*n^2 + n.

Conjectures from Colin Barker, Jan 29 2019: (Start)

G.f.: 6*x*(4 + 13*x + 2*x^2 + x^3) / (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=3:
..1. .1. .0. .3. .1. .0. .1. .0. .1. .3. .0. .0. .0. .0. .1. .0
..0. .0. .1. .0. .3. .2. .0. .2. .0. .0. .0. .0. .0. .0. .1. .3
..2. .2. .1. .1. .0. .2. .2. .3. .3. .0. .1. .2. .0. .2. .2. .3
..0. .3. .0. .2. .3. .3. .1. .3. .0. .0. .2. .3. .2. .3. .1. .3
..3. .3. .3. .2. .1. .1. .2. .3. .3. .2. .2. .1. .0. .3. .0. .0

Crossrefs

Row 5 of A269776.

Sequence in context: A297679 A202073 A107968 * A024302 A181710 A201192

Adjacent sequences: A269774 A269775 A269776 * A269778 A269779 A269780

Keyword

nonn

Author

R. H. Hardin, Mar 04 2016

Status

approved