A269643 Number of length-6 0..n arrays with no repeated value differing from the previous repeated value by other than plus two or minus 1.

16, 396, 2828, 12125, 38738, 101999, 234080, 484673, 926390, 1660883, 2825684, 4601765, 7221818, 10979255, 16237928, 23442569, 33129950, 45940763, 62632220, 84091373, 111349154, 145595135, 188193008, 240696785, 304867718, 382691939

Offset

1,1

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = n^6 + 6*n^5 + 5*n^4 + 12*n^3 - 12*n^2 + 9*n - 7 for n>2.

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

G.f.: x*(16 + 284*x + 392*x^2 + 85*x^3 - 49*x^4 + 2*x^5 - 14*x^6 + 5*x^7 - x^8) / (1 - x)^7.

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>9.

(End)

Example

Some solutions for n=3:
..1. .2. .3. .0. .2. .3. .1. .2. .1. .0. .0. .0. .1. .0. .1. .2
..2. .2. .1. .3. .0. .1. .0. .0. .1. .1. .1. .3. .2. .2. .3. .1
..2. .0. .2. .3. .0. .3. .3. .3. .0. .1. .0. .0. .0. .0. .2. .2
..3. .3. .3. .1. .1. .0. .1. .0. .2. .2. .3. .0. .2. .1. .1. .3
..2. .1. .2. .3. .3. .1. .0. .1. .0. .3. .0. .1. .1. .1. .3. .2
..1. .3. .2. .2. .1. .2. .1. .0. .2. .1. .3. .3. .0. .2. .3. .1

Crossrefs

Row 6 of A269640.

Sequence in context: A227390 A284854 A269412 * A071133 A186854 A035021

Adjacent sequences: A269640 A269641 A269642 * A269644 A269645 A269646

Keyword

nonn

Author

R. H. Hardin, Mar 02 2016

Status

approved