A269620 Number of length-4 0..n arrays with no repeated value differing from the previous repeated value by other than plus two, zero or minus 1.

15, 78, 249, 612, 1275, 2370, 4053, 6504, 9927, 14550, 20625, 28428, 38259, 50442, 65325, 83280, 104703, 130014, 159657, 194100, 233835, 279378, 331269, 390072, 456375, 530790, 613953, 706524, 809187, 922650, 1047645, 1184928, 1335279

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.

Conjectures from Colin Barker, Jan 25 2019: (Start)

G.f.: 3*x*(5 + x + 3*x^2 - x^3) / (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=8:
..2. .5. .6. .8. .5. .2. .1. .4. .1. .5. .5. .6. .0. .5. .7. .2
..2. .7. .2. .7. .2. .2. .0. .6. .0. .1. .6. .0. .3. .6. .1. .5
..6. .5. .7. .0. .2. .3. .6. .7. .0. .5. .1. .2. .5. .2. .7. .2
..3. .2. .6. .0. .5. .8. .0. .6. .7. .6. .2. .2. .4. .4. .2. .4

Crossrefs

Row 4 of A269619.

Sequence in context: A128272 A180579 A081591 * A269436 A044202 A044583

Adjacent sequences: A269617 A269618 A269619 * A269621 A269622 A269623

Keyword

nonn

Author

R. H. Hardin, Mar 01 2016

Status

approved