A014278 Number of trees on n nodes with 3 forbidden limbs of size 4, 5 and 6.

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

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