A269533 Number of length-n 0..4 arrays with no repeated value differing from the previous repeated value by other than one.

5, 25, 120, 568, 2648, 12214, 55836, 253418, 1143256, 5131592, 22934652, 102124670, 453300160, 2006497722, 8860136576, 39040820448, 171705037456, 753921273870, 3305432501828, 14473039186090, 63296720868120, 276532411704016

Offset

1,1

Links

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

Formula

Empirical: a(n) = 14*a(n-1) - 65*a(n-2) + 80*a(n-3) + 163*a(n-4) - 280*a(n-5) - 208*a(n-6).

Empirical g.f.: x*(5 - 45*x + 95*x^2 + 113*x^3 - 319*x^4 - 213*x^5) / ((1 - 4*x)^2*(1 - 6*x + x^2 + 24*x^3 + 13*x^4)). - Colin Barker, Jan 23 2019

Example

Some solutions for n=7:
..1. .2. .1. .4. .4. .3. .3. .3. .0. .4. .4. .1. .4. .1. .4. .3
..3. .0. .1. .1. .0. .3. .2. .2. .4. .4. .3. .3. .0. .0. .3. .1
..1. .4. .0. .3. .3. .4. .3. .4. .1. .2. .1. .2. .0. .3. .1. .0
..3. .3. .4. .1. .4. .0. .2. .4. .4. .3. .4. .4. .4. .0. .0. .3
..1. .0. .2. .2. .2. .4. .3. .0. .0. .0. .1. .3. .0. .2. .4. .0
..2. .0. .0. .1. .4. .3. .1. .3. .0. .4. .3. .0. .4. .3. .0. .1
..3. .4. .0. .0. .2. .4. .0. .1. .4. .1. .1. .3. .1. .1. .4. .4

Crossrefs

Column 4 of A269537.

Sequence in context: A344097 A268940 A269636 * A269405 A269674 A269602

Adjacent sequences: A269530 A269531 A269532 * A269534 A269535 A269536

Keyword

nonn

Author

R. H. Hardin, Feb 29 2016

Status

approved