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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A366415 a(n) is the number of exterior top arches (no covering arch) for semi-meanders in generation n+1 that are generated by semi-meanders with n top arches and floor(n/2) exterior top arches using the exterior arch splitting algorithm. 0
 10, 34, 78, 222, 362, 938, 1326, 3246, 4242, 10002, 12438, 28566, 34330, 77338, 90654, 201246, 231458, 507938, 575526, 1251366, 1400874, 3022890, 3350574, 7184430, 7897138, 16842802, 18382902, 39026742, 42336314, 89522234, 96600126, 203554878 (list; graph; refs; listen; history; text; internal format)
 OFFSET 4,1 COMMENTS b(n) = ((n-4)*2^floor((n-1)/2)+2)*floor(n/2) is the number of exterior top arches for all semi-meander solutions with n top arches and floor(n/2) exterior top arches. Conjecture: for n>=5, lim_{n->oo} a(n)/b(n) = 3. LINKS Table of n, a(n) for n=4..35. Michael LaCroix, Approaches to the Enumerative Theory of Meanders, 2003, pg. 31-31, Demonstrates arch splitting with semi-meander models. Index entries for linear recurrences with constant coefficients, signature (1,7,-7,-18,18,20,-20,-8,8). FORMULA For n>2: a(2*n) = (3*n-1)*((2*n-4)*2^(n-1) + 2) - (3*n-3)*((2*n-5)*2^(n-1) + 2) + a(2*n-1); a(2*n+1) = 3*n*((2*n-3)*2^n + 2) - 3*n*((2*n-4)*2^(n-1) + 2) + a(2*n). G.f.: 2*x^4*(5 + 12*x - 13*x^2 - 12*x^3 + 6*x^4)/((1 - x)^2*(1 + x)*(1 - 2*x^2)^3). - Stefano Spezia, Nov 07 2023 EXAMPLE For n=5, the number of semi-meanders with 5 top arches and 2 exterior top arches is equal to A259689(5,2) = 6: __ __ //\\ __ ____ //\\ __ ____ ///\\\ __ //\\ / /\\ ///\\\ //\\ __ //\ \ /\////\\\\, //\\///\\\, /\//\//\\\, ////\\\\/\, ///\\\//\\, ///\\/\\/\ There are 12 exterior arches for the 6 solutions. Solutions for generation n+1 using the exterior arch splitting algorithm: __ //\\ __ ____ ///\\\ __ //\\ __ /____\ ////\\\\ __ //\\ ///\\\ //\\ __ // __\\ __ __ /\/////\\\\\,//\\///\\\/\,/\/\////\\\\,///\\\//\\/\,/\///\//\\\\,//\\/\//\\/\ __ //\\ __ ____ ///\\\ __ //\\ __ /____\ ////\\\\ //\\ __ ///\\\ __ //\\ //__ \\ __ __ /////\\\\\/\,/\///\\\//\\,////\\\\/\/\,/\//\\///\\\,////\\/\\\/\,/\//\\/\//\\ These 12 solutions have 34 exterior arches. Therefore a(5) = 34. CROSSREFS Cf. A259869, A365679. Sequence in context: A155486 A225276 A008527 * A007584 A218329 A009924 Adjacent sequences: A366412 A366413 A366414 * A366416 A366417 A366418 KEYWORD nonn,easy AUTHOR Roger Ford, Oct 10 2023 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 April 22 02:54 EDT 2024. Contains 371887 sequences. (Running on oeis4.)