|
| |
|
|
A194724
|
|
Number of quaternary words either empty or beginning with the first character of the alphabet, that can be built by inserting n doublets into the initially empty word.
|
|
4
|
|
|
|
1, 1, 7, 58, 523, 4966, 48838, 492724, 5068915, 52955950, 560198962, 5987822380, 64563867454, 701383563388, 7668869344108, 84326618668648, 931894610845123, 10344218506421758, 115280448164645818, 1289346114476360188, 14467472108268263818, 162816535672067515828
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,3
|
|
|
REFERENCES
|
C. Kassel and C. Reutenauer, Algebraicity of the zeta function associated to a matrix over a free group algebra, arXiv preprint arXiv:1303.3481, 2013
|
|
|
LINKS
|
Alois P. Heinz, Table of n, a(n) for n = 0..200
|
|
|
FORMULA
|
G.f.: 3/4 + 3/(2*(2+4*sqrt(1-12*x))).
a(0) = 1, a(n) = 1/n * Sum_{j=0..n-1} C(2*n,j)*(n-j)*3^j for n>0.
|
|
|
EXAMPLE
|
a(2) = 7: aaaa, aabb, aacc, aadd, abba, acca, adda (with quaternary alphabet {a,b,c,d}).
|
|
|
MAPLE
|
a:= n-> `if` (n=0, 1, add (binomial (2*n, j) *(n-j) *3^j, j=0..n-1) /n):
seq (a(n), n=0..25);
|
|
|
MATHEMATICA
|
CoefficientList[Series[3/4+3/(2(2+4Sqrt[1-12x])), {x, 0, 30}], x] (* Harvey P. Dale, Sep 30 2012 *)
|
|
|
CROSSREFS
|
Column k=4 of A183134.
Sequence in context: A015566 A006193 A139397 * A081343 A163048 A192940
Adjacent sequences: A194721 A194722 A194723 * A194725 A194726 A194727
|
|
|
KEYWORD
|
nonn,changed
|
|
|
AUTHOR
|
Alois P. Heinz, Sep 02 2011
|
|
|
STATUS
|
approved
|
| |
|
|
