A269607 Number of length-4 0..n arrays with no repeated value differing from the previous repeated value by one or less.

8, 62, 222, 572, 1220, 2298, 3962, 6392, 9792, 14390, 20438, 28212, 38012, 50162, 65010, 82928, 104312, 129582, 159182, 193580, 233268, 278762, 330602, 389352, 455600, 529958, 613062, 705572, 808172, 921570, 1046498, 1183712, 1333992

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 + 4*n^2 - n.

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

G.f.: 2*x*(4 + 11*x - 4*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=7:
..0. .7. .6. .5. .4. .1. .1. .5. .3. .5. .0. .3. .1. .3. .4. .4
..5. .6. .4. .1. .0. .2. .4. .1. .4. .1. .3. .0. .7. .0. .6. .3
..3. .5. .6. .7. .6. .1. .6. .7. .3. .7. .4. .3. .0. .6. .0. .7
..7. .7. .6. .5. .1. .4. .2. .4. .2. .6. .7. .4. .1. .7. .1. .7

Crossrefs

Row 4 of A269606.

Sequence in context: A082179 A114028 A044527 * A296584 A198690 A056054

Adjacent sequences: A269604 A269605 A269606 * A269608 A269609 A269610

Keyword

nonn

Author

R. H. Hardin, Mar 01 2016

Status

approved