A103685 Consider the morphism 1->{1,2}, 2->{1,3}, 3->{1}; a(n) is the total number of '3' after n substitutions.

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

Offset: 0

Author

Roger L. Bagula, Mar 26 2005

Keywords

• nonn
• easy

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

• Index entries for linear recurrences with constant coefficients, signature (5,-8,6,-2).

Crossrefs

Cf. A073058, A103684.

Programs

Mathematica

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

Formula

a(n)= +5*a(n-1) -8*a(n-2) +6*a(n-3) -2*a(n-4) = a(n-1)+A115390(n). [Nov 18 2010]

G.f.: x^2 / ( (x-1)*(2*x^3-4*x^2+4*x-1) ). [Nov 18 2010]

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