A006570 - OEIS

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

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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