

A209352


Number of initially rising meander words, where each letter of the cyclic 6ary alphabet occurs n times.


2



1, 1, 16, 484, 17956, 749956, 33779344, 1603842304, 79171327876, 4026836863204, 209730177700096, 11135960392243600, 600800844868633600, 32853035097265158400, 1817225079550242841600, 101519847275313821814784, 5720749624907993103318916, 324836041052683988251601956
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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*n1)step walks on 6dimensional 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



FORMULA

a(n) = A197657(n1)^2 for n>0, a(0) = 1.


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(n1, k);
h^m +`if`(m<2, 0, h* g(m1, n, nk2))
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;


CROSSREFS



KEYWORD

nonn,walk


AUTHOR



STATUS

approved



