A269495 Number of length-4 0..n arrays with no repeated value differing from the previous repeated value by one.

14, 77, 250, 617, 1286, 2389, 4082, 6545, 9982, 14621, 20714, 28537, 38390, 50597, 65506, 83489, 104942, 130285, 159962, 194441, 234214, 279797, 331730, 390577, 456926, 531389, 614602, 707225, 809942, 923461, 1048514, 1185857, 1336270

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 + 6*n^2 + 2*n + 1.

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

G.f.: x*(14 + 7*x + 5*x^2 - 3*x^3 + x^4) / (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=6:
..2. .5. .3. .5. .6. .1. .1. .5. .5. .6. .4. .0. .5. .5. .2. .6
..1. .3. .1. .5. .2. .3. .1. .2. .5. .6. .4. .6. .1. .6. .3. .0
..3. .2. .6. .3. .1. .2. .5. .5. .1. .6. .2. .3. .3. .2. .6. .2
..1. .0. .6. .6. .0. .4. .2. .1. .2. .6. .6. .5. .0. .6. .3. .2

Crossrefs

Row 4 of A269494.

Sequence in context: A280396 A010821 A022706 * A085462 A050404 A335757

Adjacent sequences: A269492 A269493 A269494 * A269496 A269497 A269498

Keyword

nonn

Author

R. H. Hardin, Feb 28 2016

Status

approved