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A014278 Number of trees on n nodes with 3 forbidden limbs of size 4, 5 and 6. 1
0, 1, 1, 2, 3, 6, 12, 30, 67, 159, 381, 929, 2282, 5680, 14241, 36009, 91611, 234512, 603330, 1559582, 4047956, 10546556, 27570983, 72301171, 190136444, 501323021, 1324981299, 3509660618, 9315633928, 24773632117, 65999430834, 176121938800, 470720836811, 1259936118810, 3376997883966, 9063076063854 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..35.

T. Lu, The enumeration of trees with and without given limbs, Discr. Math., 154 (1996), 153-165, Example 6.

Index entries for sequences related to trees

FORMULA

G.f. (x-x^4-x^5-x^6+2*x^7)/[Product_{p>=1} (1-x^p)^a(p)], implicit form. - R. J. Mathar, Feb 27 2016

MATHEMATICA

nmax = 30; b = ConstantArray[0, nmax+1]; b[[1]] = 0; b[[2]] = 1; Do[b[[n+1]] = SeriesCoefficient[(x-x^4-x^5-x^6+2*x^7) / Product[(1 - x^p)^(b[[p+1]]), {p, 1, n-1}], {x, 0, n}], {n, 2, nmax}]; b (* Vaclav Kotesovec, Feb 28 2016 *)

CROSSREFS

Sequence in context: A145062 A300323 A261230 * A061056 A060777 A200744

Adjacent sequences:  A014275 A014276 A014277 * A014279 A014280 A014281

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified October 21 22:47 EDT 2019. Contains 328315 sequences. (Running on oeis4.)