A269615 Number of length-n 0..4 arrays with no repeated value differing from the previous repeated value by other than plus two, zero or minus 1.

5, 25, 125, 612, 2956, 14125, 66925, 314935, 1473779, 6865098, 31856590, 147352985, 679742085, 3128486473, 14370696813, 65902020548, 301787376436, 1380297559417, 6306497302225, 28787967919963, 131309246498679, 598532215284482

Offset

1,1

Links

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

Formula

Empirical: a(n) = 16*a(n-1) - 93*a(n-2) + 220*a(n-3) - 115*a(n-4) - 168*a(n-5) - 44*a(n-6) - 16*a(n-7).

Empirical g.f.: x*(5 - 55*x + 190*x^2 - 163*x^3 - 136*x^4 - 40*x^5 - 12*x^6) / ((1 - 4*x)*(1 - 12*x + 45*x^2 - 40*x^3 - 45*x^4 - 12*x^5 - 4*x^6)). - Colin Barker, Jan 25 2019

Example

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

Crossrefs

Column 4 of A269619.

Sequence in context: A267780 A228736 A126642 * A269579 A269431 A269686

Adjacent sequences: A269612 A269613 A269614 * A269616 A269617 A269618

Keyword

nonn

Author

R. H. Hardin, Mar 01 2016

Status

approved