A006570 From trees with valency <= 3. (Formerly M1475)

1, 2, 5, 15, 48, 166, 596, 2221, 8472, 32995, 130507, 523100, 2119454, 8667529, 35727261, 148285069, 619172847, 2599212499, 10963049307, 46437309218, 197454056586, 842504023722, 3606195947971, 15480329150558, 66628688247862, 287475949517326, 1243140817965661

Offset

1,2

Comments

Generating function denoted as x(t) = f(V_3;t) - 1 in Cameron page 182. - Michael Somos, Jun 13 2014

References

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Table of n, a(n) for n=1..27.

P. J. Cameron, Some treelike objects, Quart. J. Math. Oxford, 38 (1987), 155-183.

Index entries for sequences related to trees

Formula

G.f. A(x) satisfies 0 = (1 + x) * A(x)^2 + (2*x - 2) * A(x) + (1 + x) * A(x^2) + 2*x. - Michael Somos, Jun 13 2014

Example

G.f. = x + 2*x^2 + 5*x^3 + 15*x^4 + 48*x^5 + 166*x^6 + 596*x^7 + 2221*x^8 + ...

Mathematica

m = 30; A[_] = 0;
Do[A[x_] = (2x + (1+x) A[x]^2 + (1+x) A[x^2])/(2(1-x)) + O[x]^m // Normal, {m}];
CoefficientList[A[x], x] (* Jean-François Alcover, Oct 23 2019 *)

Prog

(PARI) {a(n) = my(A); A = x + O(x^2); for(k=2, n, A = truncate(A) + x * O(x^k); A += x - (1-x)*A + (1+x)/2 * (A^2 + subst(A, x, x^2))); polcoeff(A, n)}; /* Michael Somos, Jun 13 2014 */

Crossrefs

Sequence in context: A145072 A149927 A035350 * A149928 A003430 A149929

Adjacent sequences: A006567 A006568 A006569 * A006571 A006572 A006573

Keyword

nonn

Author

N. J. A. Sloane.

Extensions

a(10)-a(37) from Michael Somos, Jun 13 2014

Status

approved