OFFSET
1,1
COMMENTS
f(g,h) = per(B), the permanent of the (0,1)-matrix B of size g X g+h with b(i,j)=1 if and only if i <= j <= i+h. See A079908 for more information.
With offset 4, number of 132-avoiding two-stack sortable permutations which contain exactly one subsequence of type 123.
LINKS
Harvey P. Dale, Table of n, a(n) for n = 1..1000
Jaap Spies, Dancing School Problems, Nieuw Archief voor Wiskunde 5/7 nr. 4, Dec 2006, pp. 283-285.
E. S. Egge and T. Mansour, 132-avoiding two-stack sortable permutations....
Index entries for linear recurrences with constant coefficients, signature (3,-2,-1,1).
FORMULA
a(n) = a(n-1)+a(n-2)+n+1, a(1)=3, a(2)=7.
G.f.: 1/((1-x)^2*(1-x-x^2)).
F(n+5) - n - 4, F(n) = A000045(n).
a(n) = 3*a(n-1)-2*a(n-2)-a(n-3)+a(n-4). - Wesley Ivan Hurt, Dec 03 2021
MAPLE
with(genfunc): Fz := 1/((-1+z)^2 * (1-z-z^2)); seq(rgf_term(Fz, z, n), n=1..30);
MATHEMATICA
CoefficientList[Series[(-z^3 + z^2 + 2*z - 3)/((z - 1)^2 (z^2 + z - 1)), {z, 0, 100}], z] (* Vladimir Joseph Stephan Orlovsky, Jul 08 2011 *)
LinearRecurrence[{3, -2, -1, 1}, {3, 7, 14, 26}, 40] (* Harvey P. Dale, Oct 17 2022 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Jaap Spies, Jan 28 2003
EXTENSIONS
More terms from Jaap Spies, Dec 15 2006
STATUS
approved