A269468 Number of length-4 0..n arrays with no repeated value equal to the previous repeated value.

10, 66, 228, 580, 1230, 2310, 3976, 6408, 9810, 14410, 20460, 28236, 38038, 50190, 65040, 82960, 104346, 129618, 159220, 193620, 233310, 278806, 330648, 389400, 455650, 530010, 613116, 705628, 808230, 921630, 1046560, 1183776, 1334058

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 + 4*n^2 + n.

Conjectures from Colin Barker, Jan 23 2019: (Start)

G.f.: 2*x*(5 + 8*x - x^2) / (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>5.

(End)

Example

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

Crossrefs

Row 4 of A269467.

Sequence in context: A159838 A269679 A211056 * A024391 A074362 A080421

Adjacent sequences: A269465 A269466 A269467 * A269469 A269470 A269471

Keyword

nonn

Author

R. H. Hardin, Feb 27 2016

Status

approved