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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A209352 Number of initially rising meander words, where each letter of the cyclic 6-ary alphabet occurs n times. 2
 1, 1, 16, 484, 17956, 749956, 33779344, 1603842304, 79171327876, 4026836863204, 209730177700096, 11135960392243600, 600800844868633600, 32853035097265158400, 1817225079550242841600, 101519847275313821814784, 5720749624907993103318916, 324836041052683988251601956 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS In a meander word letters of neighboring positions have to be neighbors in the alphabet, where in a cyclic alphabet the first and the last letters are considered neighbors too. The words are not considered cyclic here. A word is initially rising if it is empty or if it begins with the first letter of the alphabet that can only be followed by the second letter in this word position. a(n) is also the number of (6*n-1)-step walks on 6-dimensional cubic lattice from (1,0,...,0) to (n,n,...,n) with positive unit steps in all dimensions such that the indices of dimensions used in consecutive steps differ by 1 or are in the set {1,6}. LINKS Alois P. Heinz, Table of n, a(n) for n = 0..500 FORMULA a(n) = A197657(n-1)^2 for n>0, a(0) = 1. a(n) ~ 3 * 2^(6*n - 4) / (Pi^2 * n^2). - Vaclav Kotesovec, May 14 2020 EXAMPLE a(0) = 1: the empty word. a(1) = 1 = |{abcdef}|. a(2) = 16 = |{ababcdcdefef, abafedcbcdef, abafefedcbcd, abafefedcdcb, abcbafedcdef, abcbafefedcd, abcbcdedefaf, abcbcdefafed, abcdcbafedef, abcdcbafefed, abcdcdefefab, abcdedcbafef, abcdefabcdef, abcdefafedcb, abcdefedcbaf, abcdefefabcd}|. MAPLE g:= proc(m, n, k) local h; h:= binomial(n-1, k); h^m +`if`(m<2, 0, h* g(m-1, n, n-k-2)) end: a:= n-> add(g(3, n, k), k=0..n)^2: seq(a(n), n=0..30); MATHEMATICA g[m_, n_, k_] := g[m, n, k] = With[{h = Binomial[n - 1, k]}, h^m + If[m < 2, 0, h g[m - 1, n, n - k - 2]]]; a[n_] := Sum[g[3, n, k], {k, 0, n}]^2; a /@ Range[0, 30] (* Jean-François Alcover, May 14 2020, after Maple *) CROSSREFS Column k=6 of A209349. Cf. A197657. Sequence in context: A254633 A283327 A185367 * A209392 A209022 A209057 Adjacent sequences: A209349 A209350 A209351 * A209353 A209354 A209355 KEYWORD nonn,walk AUTHOR Alois P. Heinz, Mar 06 2012 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 November 29 10:25 EST 2023. Contains 367429 sequences. (Running on oeis4.)