A106362 Number of rooted planar trees in which no branch is identical to its adjacent neighbor.

1, 1, 1, 2, 4, 10, 28, 77, 221, 650, 1951, 5920, 18211, 56509, 176919, 557786, 1769966, 5647568, 18110734, 58335561, 188658338, 612337013, 1994058293, 6513153445, 21332562178, 70048092196, 230550762108, 760462920317

Offset

1,4

Links

Table of n, a(n) for n=1..28.

Index entries for sequences related to rooted trees

Formula

G.f.: x+x*B(x) where B(x) is g.f. of CycleBG transform of A106361.

CycleBG transform T(A) = invMOEBIUS(invEULER(Carlitz(A)) + A(x^2) - A) + A.

Carlitz transform T(A(x)) has g.f. 1/(1-sum(k>0, (-1)^(k+1)*A(x^k))).

Crossrefs

Cf. A003239, A106363.

Sequence in context: A128933 A173781 A340825 * A271896 A148109 A099216

Adjacent sequences: A106359 A106360 A106361 * A106363 A106364 A106365

Keyword

nonn

Author

Christian G. Bower, Apr 29 2005

Status

approved