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A003609 Symmetries in planted (1,3) trees on 2n vertices.
(Formerly M0383)
8
1, 2, 2, 10, 14, 42, 90, 354, 758, 2290, 6002, 18410, 51310, 154106, 449322, 1384962, 4089174, 12475362, 37746786, 116037642, 355367310, 1097869386, 3393063162, 10546081122, 32810171382, 102465452754, 320522209490, 1005428474218 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

Kathleen A. McKeon, The expected number of symmetries in locally-restricted trees I, pp. 849-860 of Y. Alavi et al., eds., Graph Theory, Combinatorics and Applications. Wiley, NY, 2 vols., 1991.

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..28.

Sean A. Irvine, Java program (github)

Kathleen A. McKeon, Letter to N. J. A. Sloane, July 25 1991

Kathleen A. McKeon, The expected number of symmetries in locally-restricted trees I, pp. 849-860 of Y. Alavi et al., eds., Graph Theory, Combinatorics and Applications. Wiley, NY, 2 vols., 1991. [Annotated scanned copy]

Index entries for sequences related to rooted trees

Index entries for sequences related to trees

EXAMPLE

G.f. = x + 2*x^2 + 2*x^3 + 10*x^4 + 14*x^5 + 42*x^6 + 90*x^7 + ... - Michael Somos, Mar 12 2021

PROG

(PARI) {a(n) = my(A, m); A = x + O(x^2); m = 1; while(n >= (m*=2), A = (1 - sqrt(1 - 2*x*y + y*(y-2)*substvec(A, [x, y], [x^2, y^2])))/y); 2^(n-1) * subst(polcoeff(A, n), y, 1/2)}; /* Michael Somos, Mar 12 2021 */

CROSSREFS

Sequence in context: A048153 A015623 A164124 * A307538 A316200 A179789

Adjacent sequences:  A003606 A003607 A003608 * A003610 A003611 A003612

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Mira Bernstein

EXTENSIONS

More terms from Sean A. Irvine, Feb 24 2019

STATUS

approved

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Last modified April 15 04:04 EDT 2021. Contains 342974 sequences. (Running on oeis4.)