A374558 Number of maximal matchings in the n-Dorogovtsev-Goltsev-Mendes graph.

1, 3, 11, 566, 18843648, 91440753373003907072, 1315744819459109156721305425009269045447614039663170289664

Offset

0,2

Comments

Using the indexing convention that DGM(0) = P_2.

Term a(7) has 168 decimal digits and a(8) has 499 decimal digits. - Andrew Howroyd, Jun 08 2025

Links

Andrew Howroyd, Table of n, a(n) for n = 0..8

Eric Weisstein's World of Mathematics, Dorogovtsev-Goltsev-Mendes Graph.

Eric Weisstein's World of Mathematics, Maximal Independent Edge Set.

Mathematica

#3 + 2 #4 & @@@ NestList[Function[{m0, m1, m2, p, e}, {2 m0^2 m1 + m0 e^2, 3 m0 m1^2 + m0^2 m2 + m1 e^2 + m0 p e, 6 m0 m1 m2 + 2 m1^3 + m2 e^2 + 2 m1 p e + m0 p^2, m2 e^2 + m1 p e + m0 p^2 + p^2 e, m0 p e + m1 e^2}] @@ # &, {1, 0, 1, 0, 1}, 8] (* Eric W. Weisstein, Sep 03 2025 *)

Prog

(PARI)
step(S)={my([m0, m1, m2, p, e]=S); [2*m0^2*m1 + m0*e^2, 3*m0*m1^2 + m0^2*m2 + m1*e^2 + m0*p*e, 6*m0*m1*m2 + 2*m1^3 + m2*e^2 + 2*m1*p*e + m0*p^2, m2*e^2 + m1*p*e + m0*p^2 + p^2*e, m0*p*e + m1*e^2]}
a(n)={my(S=[1, 0, 1, 0, 1]); for(i=1, n, S=step(S)); S[3] + 2*S[4]} \\ Andrew Howroyd, Jun 08 2025

Crossrefs

Sequence in context: A111130 A337415 A264725 * A088579 A344946 A368618

Adjacent sequences: A374555 A374556 A374557 * A374559 A374560 A374561

Keyword

nonn

Author

Eric W. Weisstein, Jul 11 2024

Extensions

a(5) onwards from Andrew Howroyd, Jun 08 2025

Status

approved