A269584 Number of length-4 0..n arrays with no repeated value differing from the previous repeated value by more than one.

16, 79, 250, 613, 1276, 2371, 4054, 6505, 9928, 14551, 20626, 28429, 38260, 50443, 65326, 83281, 104704, 130015, 159658, 194101, 233836, 279379, 331270, 390073, 456376, 530791, 613954, 706525, 809188, 922651, 1047646, 1184929, 1335280

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 + 5*n^2 + 5*n + 1.

Conjectures from Colin Barker, Jan 24 2019: (Start)

G.f.: x*(16 - x + 15*x^2 - 7*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:
..4. .0. .1. .6. .0. .1. .1. .2. .1. .3. .5. .1. .2. .3. .0. .6
..0. .5. .3. .4. .3. .5. .2. .1. .2. .2. .2. .3. .5. .4. .6. .2
..1. .6. .0. .1. .6. .4. .1. .1. .5. .6. .4. .1. .3. .0. .2. .2
..2. .6. .4. .0. .4. .1. .5. .0. .0. .0. .3. .0. .2. .5. .2. .0

Crossrefs

Row 4 of A269583.

Sequence in context: A250231 A212896 A250279 * A044203 A044584 A111732

Adjacent sequences: A269581 A269582 A269583 * A269585 A269586 A269587

Keyword

nonn

Author

R. H. Hardin, Mar 01 2016

Status

approved