A269660 Number of length-7 0..n arrays with no adjacent pair x,x+1 repeated.

64, 1710, 14596, 73348, 269472, 803434, 2061940, 4725456, 9911008, 19355302, 35643204, 62486620, 105058816, 170389218, 267823732, 409555624, 611232000, 892640926, 1278484228, 1799241012, 2492126944, 3402154330, 4583298036

Offset

1,1

Links

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

Formula

Empirical: a(n) = n^7 + 7*n^6 + 21*n^5 + 25*n^4 + 5*n^3 + 2*n^2 + 11*n - 8.

Conjectures from Colin Barker, Jan 26 2019: (Start)

G.f.: 2*x*(32 + 599*x + 1354*x^2 + 438*x^3 + 48*x^4 + 71*x^5 - 26*x^6 + 4*x^7) / (1 - x)^8.

a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.

(End)

Example

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

Crossrefs

Row 7 of A269656.

Sequence in context: A317010 A316875 A317603 * A234240 A017115 A269203

Adjacent sequences: A269657 A269658 A269659 * A269661 A269662 A269663

Keyword

nonn

Author

R. H. Hardin, Mar 02 2016

Status

approved