OFFSET
0,2
COMMENTS
Number of 3-permutations of n elements avoiding the patterns 132, 321. See Bonichon and Sun. - Michel Marcus, Aug 19 2022
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Nicolas Bonichon and Pierre-Jean Morel, Baxter d-permutations and other pattern avoiding classes, arXiv:2202.12677 [math.CO], 2022.
Nathan Sun, On d-permutations and Pattern Avoidance Classes, arXiv:2208.08506 [math.CO], 2022.
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
FORMULA
a(n) = A051925(n+1) + 1. - Alex Ratushnyak, Jun 27 2012
From Vincenzo Librandi, Jun 28 2012: (Start)
G.f.: (1 + 2*x^2 - x^3)/(1-x)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).
a(n) = (2*n^3 + 9*n^2 + 7*n + 6)/6. (End)
a(n) = A000330(n+1) - n. - John Tyler Rascoe, Jun 24 2022
MATHEMATICA
CoefficientList[Series[(1+2*x^2-x^3)/((1-x)^4), {x, 0, 50}], x] (* Vincenzo Librandi, Jun 28 2012 *)
LinearRecurrence[{4, -6, 4, -1}, {1, 4, 12, 27}, 50] (* Harvey P. Dale, Aug 22 2015 *)
PROG
(Magma) I:=[1, 4, 12, 27]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..40]]; // Vincenzo Librandi, Jun 28 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Patternfinder(AT)webtv.net (Robert Newstedt)
STATUS
approved