A269679 Number of length-4 0..n arrays with no repeated value differing from the previous repeated value by other than plus or minus one modulo n+1.

10, 66, 224, 570, 1212, 2282, 3936, 6354, 9740, 14322, 20352, 28106, 37884, 50010, 64832, 82722, 104076, 129314, 158880, 193242, 232892, 278346, 330144, 388850, 455052, 529362, 612416, 704874, 807420, 920762, 1045632, 1182786, 1333004

Offset

1,1

Links

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

Formula

Empirical: a(n) = n^4 + 4*n^3 + 3*n^2 + 2*n + 2 for n>1.

Conjectures from Colin Barker, Jan 26 2019: (Start)

G.f.: 2*x*(5 + 8*x - 3*x^2 + 5*x^3 - 4*x^4 + x^5) / (1 - x)^5.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>6.

(End)

Example

Some solutions for n=3:
..1. .3. .2. .3. .2. .1. .3. .3. .2. .0. .2. .3. .3. .2. .2. .2
..3. .1. .1. .0. .0. .2. .2. .0. .1. .0. .2. .2. .2. .2. .1. .3
..0. .0. .3. .1. .2. .0. .2. .1. .2. .1. .0. .3. .1. .3. .3. .2
..2. .2. .0. .0. .2. .0. .1. .3. .2. .2. .2. .2. .0. .2. .3. .2

Crossrefs

Row 4 of A269678.

Sequence in context: A344060 A140362 A159838 * A211056 A269468 A024391

Adjacent sequences: A269676 A269677 A269678 * A269680 A269681 A269682

Keyword

nonn

Author

R. H. Hardin, Mar 03 2016

Status

approved