A269636 Number of length-n 0..4 arrays with no repeated value differing from the previous repeated value by other than plus two or minus 1.

5, 25, 120, 567, 2637, 12125, 55225, 249600, 1120868, 5006144, 22255415, 98544130, 434827380, 1912861067, 8392454605, 36733957588, 160447861687, 699496998228, 3044446874255, 13230474539089, 57418454111103, 248881927670961

Offset

1,1

Links

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

Formula

Empirical: a(n) = 13*a(n-1) - 51*a(n-2) + 15*a(n-3) + 240*a(n-4) - 96*a(n-5) - 509*a(n-6) - 268*a(n-7).

Empirical g.f.: x*(5 - 40*x + 50*x^2 + 207*x^3 - 189*x^4 - 559*x^5 - 273*x^6) / ((1 - 4*x)*(1 - 9*x + 15*x^2 + 45*x^3 - 60*x^4 - 144*x^5 - 67*x^6)). - Colin Barker, Jan 25 2019

Example

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

Crossrefs

Column 4 of A269640.

Sequence in context: A110212 A344097 A268940 * A269533 A269405 A269674

Adjacent sequences: A269633 A269634 A269635 * A269637 A269638 A269639

Keyword

nonn

Author

R. H. Hardin, Mar 02 2016

Status

approved