A269538 Number of length-4 0..n arrays with no repeated value differing from the previous repeated value by other than one.

10, 64, 222, 568, 1210, 2280, 3934, 6352, 9738, 14320, 20350, 28104, 37882, 50008, 64830, 82720, 104074, 129312, 158878, 193240, 232890, 278344, 330142, 388848, 455050, 529360, 612414, 704872, 807418, 920760, 1045630, 1182784, 1333002

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 + 3*n^2 + 2*n.

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

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

Crossrefs

Row 4 of A269537.

Sequence in context: A162473 A138661 A341681 * A178256 A036426 A245068

Adjacent sequences: A269535 A269536 A269537 * A269539 A269540 A269541

Keyword

nonn

Author

R. H. Hardin, Feb 29 2016

Status

approved