OFFSET
0,2
COMMENTS
The sequence is generated by a rational function, in particular, a quotient of two determinants.
LINKS
Lily Yen, Table of n, a(n) for n = 0..1000
Lily Yen, Crossings and Nestings for Arc-Coloured Permutations, arXiv:1211.3472 [math.CO], 2012-2013.
Index entries for linear recurrences with constant coefficients, signature (7,-6,-4).
FORMULA
G.f.: (1 - 5*x)/(1 - 7*x + 6*x^2 + 4*x^3).
a(n) = 7*a(n-1) - 6*a(n-2) - 4*a(n-3) for n>2. - Colin Barker, Jun 22 2019
EXAMPLE
For n=4, the a(4) = 224 solutions are 24 permutations, 8 of which can be colored in 4 ways each, 8 in 8 ways each, and 8 in 16 ways each, thus resulting in 8 * (4+8+16) = 224.
PROG
(PARI) Vec((1 - 5*x) / (1 - 7*x + 6*x^2 + 4*x^3) + O(x^40)) \\ Colin Barker, Jun 22 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Lily Yen, Nov 23 2012
EXTENSIONS
Name modified by Lily Yen, Apr 23 2013
STATUS
approved