

A242452


Number of length n words on {1,2,3} with no more than one consecutive 1 and no more than two consecutive 2's and no more than three consecutive 3's.


4



1, 3, 8, 21, 54, 140, 362, 937, 2425, 6275, 16239, 42024, 108751, 281430, 728295, 1884709, 4877320, 12621710, 32662931, 84526348, 218740428, 566064618, 1464883079, 3790878933, 9810177543, 25387142435, 65697791726, 170015189725, 439971633412, 1138574962157
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,2


LINKS

Fung Lam, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,2,4,3,2).


FORMULA

G.f.: (1 + x)*(1 + x^2)*(1 + x + x^2)/(1  x  2*x^2  4*x^3  3*x^4  2*x^5).


EXAMPLE

a(3) = 21 because there are 27 length 3 words on {1,2,3} but we don't count: 111, 112, 113, 211, 222, 311.


MATHEMATICA

nn=20; CoefficientList[Series[1/(1Sum[v[i]/(1+v[i])/.v[i]>(zz^(i+1))/(1z), {i, 1, 3}]), {z, 0, nn}], z]
(* replacing the 3 in this code with a positive integer k will return the number of words on {1, 2, ..., k} with no more than one consecutive 1 and no more than two consecutive 2's and ... no more than k consecutive k's *)


CROSSREFS

Cf. A000931 (binary words with at most one consecutive 1 and two consecutive 2's; offset=8 for n>0).
Cf. A007283 (ternary words with no consecutive like letters).
Column k=3 of A242464.
Sequence in context: A127358 A077849 A135473 * A190139 A005580 A292619
Adjacent sequences: A242449 A242450 A242451 * A242453 A242454 A242455


KEYWORD

nonn,easy


AUTHOR

Geoffrey Critzer and Alois P. Heinz, May 14 2014


STATUS

approved



