A047732 First differences are A005563.

1, 4, 12, 27, 51, 86, 134, 197, 277, 376, 496, 639, 807, 1002, 1226, 1481, 1769, 2092, 2452, 2851, 3291, 3774, 4302, 4877, 5501, 6176, 6904, 7687, 8527, 9426, 10386, 11409, 12497, 13652, 14876, 16171, 17539, 18982, 20502, 22101, 23781, 25544, 27392, 29327

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

Cf. A000330, A005563, A051925.

Sequence in context: A266958 A057306 A212973 * A104385 A213760 A062479

Adjacent sequences: A047729 A047730 A047731 * A047733 A047734 A047735

Keyword

nonn,easy

Author

Patternfinder(AT)webtv.net (Robert Newstedt)

Status

approved