login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A269660
Number of length-7 0..n arrays with no adjacent pair x,x+1 repeated.
2
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
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
KEYWORD
nonn
AUTHOR
R. H. Hardin, Mar 02 2016
STATUS
approved