OFFSET
0,2
COMMENTS
Row sums of triangle A131897.
Binomial transform of (1, 4, 2, 2, 2, ...).
a(n), n > 0, is the number of maximal subsemigroups of the Motzkin monoid of degree n + 1. - James Mitchell and Wilf A. Wilson, Jul 21 2017
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
James East, Jitender Kumar, James D. Mitchell, and Wilf A. Wilson, Maximal subsemigroups of finite transformation and partition monoids, arXiv:1706.04967 [math.GR], 2017. [From James Mitchell and Wilf A. Wilson, Jul 21 2017]
Index entries for linear recurrences with constant coefficients, signature (4,-5,2).
FORMULA
G.f.: ( -1-x+4*x^2 ) / ( (2*x-1)*(x-1)^2 ). - R. J. Mathar, Jul 03 2011
a(n) = 4*a(n-1) -5*a(n-2) +2*a(n-3). - Vincenzo Librandi, Jul 05 2012
EXAMPLE
a(3) = 21 = sum of row 3 terms of triangle A131897: (11 + 4 + 2 + 4).
a(3) = 21 = (1, 3, 3, 1) dot (1, 4, 2, 2) = (1 + 12 + 6 + 2).
MATHEMATICA
CoefficientList[Series[(-1-x+4*x^2)/((2*x-1)*(x-1)^2), {x, 0, 40}], x] (* Vincenzo Librandi, Jul 05 2012 *)
PROG
(Magma) I:=[1, 5, 11]; [n le 3 select I[n] else 4*Self(n-1)-5*Self(n-2)+2*Self(n-3): n in [1..40]]; // Vincenzo Librandi, Jul 05 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Gary W. Adamson, Jul 25 2007
EXTENSIONS
New definition by R. J. Mathar, Jul 03 2011
STATUS
approved