The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A079921 Solution to the Dancing School Problem with n girls and n+2 boys: f(n,2). 1
 3, 7, 14, 26, 46, 79, 133, 221, 364, 596, 972, 1581, 2567, 4163, 6746, 10926, 17690, 28635, 46345, 75001, 121368, 196392, 317784, 514201, 832011, 1346239, 2178278, 3524546, 5702854, 9227431, 14930317, 24157781, 39088132, 63245948, 102334116, 165580101 (list; graph; refs; listen; history; text; internal format)
 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. Jaap Spies, Dancing School Problems, Permanent solutions of Problem 29. 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 Cf. A000045, A079908-A079928, A001924. Cf. Essentially the same as A001924. Sequence in context: A036830 A014153 A001924 * A369115 A293767 A014168 Adjacent sequences: A079918 A079919 A079920 * A079922 A079923 A079924 KEYWORD nonn AUTHOR Jaap Spies, Jan 28 2003 EXTENSIONS More terms from Jaap Spies, Dec 15 2006 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 19 03:30 EDT 2024. Contains 376004 sequences. (Running on oeis4.)