0,2

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

V. A. Liskovets, A census of nonisomorphic planar maps, in Algebraic Methods in Graph Theory, Vol. II, ed. L. Lovasz and V. T. Sos, North-Holland, 1981.

V. A. Liskovets, Enumeration of nonisomorphic planar maps, Selecta Math. Sovietica, 4 (No. 4, 1985), 303-323.

Walsh, T. R. S., Generating nonisomorphic maps without storing them. SIAM J. Algebraic Discrete Methods 4 (1983), no. 2, 161-178.

T. R. S. Walsh, personal communication.

Wormald, Nicholas C., Counting unrooted planar maps. Discrete Math. 36 (1981), no. 2, 205-225.

V. A. Liskovets, Enumerative formulae for unrooted planar maps: a pattern, Electron. J. Combin., 11:1 (2004), R88.

For n>0, a(n)=(1/2n)[A'(n)+sum_{k<n,k|n}phi(n/k)binomial(k+2,2)A'(k)]+q(n) where phi(n) is the Euler function A000010, q(n)=(n+3)A'(n-1/2)/4 if n is odd and q(n)=(n-1)A'(n-2/2)/4 if n is even, where A'(n)=A000168(n), the number of rooted maps. - Valery A. Liskovets (liskov(AT)im.bas-net.by), May 27 2006

Equivalently, a(n)=(1/2n)[2*3^n/((n+1)(n+2))*binomial(2n,n) +sum_{k<n,k|n}phi(n/k)3^k*binomial(2k,k)]+q(n) where q(n)=2*3^((n-1)/2)/(n+1)*binomial(n-1,(n-1)/2) if n is odd and q(n)=2(n-1)*3^((n-2)/2)/(n(n+2))*binomial(n-2,(n-2)/2) if n is even. - Valery A. Liskovets (liskov(AT)im.bas-net.by), May 27 2006

with (numtheory): a:= n-> `if` (n=0, 1, floor (2*3^n /(n+1)/(n+2) *binomial(2*n, n) +add (phi(n/t) *3^t *binomial(2*t, t), t=divisors(n) minus {n}))/2/n +`if` (irem(n, 2)=1, 2*3^((n-1)/2) /(n+1) *binomial(n-1, (n-1)/2), 2*(n-1) *3^((n-2)/2) /n/(n+2) *binomial(n-2, (n-2)/2))): seq (a(n), n=0..30); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Apr 24 2009]

Cf. A000168.

Sequence in context: A030809 A030958 A030885 this_sequence A003322 A030952 A030861

Adjacent sequences: A006381 A006382 A006383 this_sequence A006385 A006386 A006387

nonn,nice

N. J. A. Sloane (njas(AT)research.att.com).

More terms from Alois P. Heinz (heinz(AT)hs-heilbronn.de), Apr 24 2009