The OEIS is supported by the many generous donors to the OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A164991 Number of triangular involutions of n. A triangular involution is a square involution with at most three faces. 2
 1, 1, 3, 6, 13, 26, 54, 108, 221, 442, 898, 1796, 3634, 7268, 14668, 29336, 59101, 118202, 237834, 475668, 956198, 1912396, 3841588, 7683176, 15425138, 30850276, 61908564, 123817128, 248377156, 496754312 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS The sequence 2^(n+1) - binomial(n, floor(n/2)), which begins 1,3,6,... has Hankel transform (-1)^n*(2*n+1) (A157142). - Paul Barry, Nov 03 2010 For n >= 2 also row sums of A258445. - Wolfdieter Lang, Jun 27 2015 REFERENCES F. Disanto, A. Frosini, S. Rinaldi, Square Involutions, Proceedings of Permutation Patterns, July, 13-17 2009, Florence. T. Mansour, S. Severini, Grid polygons from permutations and their enumeration by the kernel method, 19th Conference on Formal Power Series and Algebraic Combinatorics, Tianjin, China, July 2-6, 2007. LINKS F. Disanto, A. Frosini, S. Rinaldi, Square involutions, J. Int. Seq. 14 (2011) # 11.3.5. T. Mansour, S. Severini, Grid polygons from permutations and their enumeration by the kernel method, arXiv:math/0603225 [math.CO], 2006. FORMULA a(n) = 2^(n-1) - binomial(n-2, floor((n-2)/2)) for n>1, a(1)=1. From Wolfdieter Lang, Jun 27 2015: (Start) a(n) = Sum_{k = 1..2*n-3} A258445(n-1, k), n >= 2. a(2*k+1) = 4*Sum_{j = 0..(k-2)} binomial(2*k-1,j) + 3*binomial(2*k-1,k-1), k >= 1. a(2*k) = 4*Sum_{j = 0..(k-2)} binomial(2*(k-1),j) + binomial(2*(k-1),k-1), k >= 1. (End) (-n+1)*a(n) + 2*(n-1)*a(n-1) + 4*(n-4)*a(n-2) + 8*(-n+4)*a(n-3) = 0. - R. J. Mathar, Aug 09 2017 MATHEMATICA Join[{1}, Table[2^(n-1)-Binomial[n-2, Floor[(n-2)/2]], {n, 2, 30}]] (* Harvey P. Dale, Dec 26 2015 *) PROG (PARI) a(n) =  2^(n-1) - binomial(n-2, (n-2)\2) \\ Michel Marcus, May 27 2013 CROSSREFS Cf. A128652, A128650, A258445. Sequence in context: A125049 A267581 A320733 * A213255 A215985 A215986 Adjacent sequences:  A164988 A164989 A164990 * A164992 A164993 A164994 KEYWORD nonn,easy AUTHOR Simone Rinaldi (rinaldi(AT)unisi.it), Sep 04 2009 STATUS approved

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

Last modified July 5 05:47 EDT 2022. Contains 355087 sequences. (Running on oeis4.)