A003609 Symmetries in planted (1,3) trees on 2n vertices. (Formerly M0383)

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

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 * A366131 A307538 A316200

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