A106362 - OEIS

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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 (list; graph; refs; listen; history; text; internal format)

	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+xB(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`

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Last modified May 23 11:27 EDT 2022. Contains 353975 sequences. (Running on oeis4.)