OFFSET
1,2
COMMENTS
a(2n) is the number of maximal subsemigroups of the planar partition monoid of degree n.
LINKS
Wilf A. Wilson, Table of n, a(n) for n = 1..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.
Index entries for linear recurrences with constant coefficients, signature (3,-2,-1,1).
FORMULA
a(n) = 2 * A000045(n - 1) + 2n - 3, n > 2.
From Colin Barker, Jul 21 2017: (Start)
G.f.: x*(1 + x)*(1 - 2*x + 3*x^2 - 4*x^3 + x^4) / ((1 - x)^2*(1 - x - x^2)).
a(n) = -5 + (2^(-n)*((1-sqrt(5))^n*(1+sqrt(5)) + (-1+sqrt(5))*(1+sqrt(5))^n)) / sqrt(5) + 2*(1+n) for n>2.
a(n) = 3*a(n-1) - 2*a(n-2) - a(n-3) + a(n-4) for n>6.
(End)
MATHEMATICA
{1, 2}~Join~Table[2 Fibonacci[n - 1] + 2 n - 3, {n, 3, 39}] (* Michael De Vlieger, Jul 21 2017 *)
PROG
(PARI) Vec(x*(1 + x)*(1 - 2*x + 3*x^2 - 4*x^3 + x^4) / ((1 - x)^2*(1 - x - x^2)) + O(x^50)) \\ Colin Barker, Jul 21 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
James Mitchell and Wilf A. Wilson, Jul 21 2017
STATUS
approved