

A103685


Consider the morphism 1>{1,2}, 2>{1,3}, 3>{1}; a(n) is the total number of '3' after n substitutions.


3



0, 0, 1, 5, 17, 51, 147, 419, 1191, 3383, 9607, 27279, 77455, 219919, 624415, 1772895, 5033759, 14292287, 40579903, 115217983, 327136895, 928835455, 2637230207, 7487852799, 21260161279, 60363694335, 171389837823, 486624896511, 1381667623423, 3922950583295
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,4


COMMENTS

Examples of the morphism starting with {1} are shown in A103684. Counting the total number of '1' in rows 1 to n of A103684 yields 1, 3, 8,... = A073357(n+1),
counting the total number of '2' in rows 1 to n yields 0, 1, 4,.. = A115390(n+1),
and counting the total number '3' in rows 1 to n yields a(n), the sequence here.
Inverse binomial transform yields 0, 0, 1, 2, 3, 6, 11, 20,..., a variant of A001590 [Nov 18 2010]


LINKS



FORMULA

a(n)= +5*a(n1) 8*a(n2) +6*a(n3) 2*a(n4) = a(n1)+A115390(n). [Nov 18 2010]
G.f.: x^2 / ( (x1)*(2*x^34*x^2+4*x1) ). [Nov 18 2010]


MATHEMATICA

LinearRecurrence[{5, 8, 6, 2}, {0, 0, 1, 5}, 30] (* Harvey P. Dale, Nov 10 2011 *)


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



EXTENSIONS

Depleted by the information already in A073357 and A115390; corrected image of {2} in the defn.  The Assoc. Eds. of the OEIS, Nov 18 2010


STATUS

approved



