A269496 Number of length-5 0..n arrays with no repeated value differing from the previous repeated value by one.

24, 215, 964, 3021, 7616, 16579, 32460, 58649, 99496, 160431, 248084, 370405, 536784, 758171, 1047196, 1418289, 1887800, 2474119, 3197796, 4081661, 5150944, 6433395, 7959404, 9762121, 11877576, 14344799, 17205940, 20506389, 24294896

Offset

1,1

Links

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

Formula

Empirical: a(n) = n^5 + 5*n^4 + 10*n^3 + 4*n^2 + 3*n + 1.

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

G.f.: x*(24 + 71*x + 34*x^2 - 18*x^3 + 10*x^4 - x^5) / (1 - x)^6.

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6. (End)

Conjectured e.g.f.: exp(x)*(1 + 23*x+ 84*x^2 + 65*x^3 + 15*x^4 + x^5) - 1. - Stefano Spezia, Feb 20 2025

Example

Some solutions for n=6:
..3. .0. .3. .3. .4. .2. .3. .4. .2. .6. .5. .4. .6. .1. .5. .5
..5. .1. .3. .0. .6. .2. .3. .3. .1. .3. .4. .2. .2. .4. .1. .3
..1. .6. .3. .1. .0. .5. .2. .4. .0. .4. .1. .0. .0. .5. .5. .6
..6. .2. .4. .5. .6. .1. .4. .2. .4. .1. .0. .6. .1. .4. .3. .6
..5. .5. .1. .6. .5. .5. .6. .3. .3. .5. .2. .1. .4. .1. .4. .5

Crossrefs

Row 5 of A269494.

Sequence in context: A381327 A050222 A169635 * A376552 A221434 A008655

Adjacent sequences: A269493 A269494 A269495 * A269497 A269498 A269499

Keyword

nonn

Author

R. H. Hardin, Feb 28 2016

Status

approved