A014273 Number of trees on n nodes with forbidden limbs.

0, 1, 2, 5, 19, 73, 297, 1256, 5467, 24368, 110610, 509715, 2377978, 11210451, 53318599, 255537199, 1232866889, 5982965779, 29185293329, 143026402189, 703829126231, 3476496240860, 17230140895115, 85659915381510, 427065111704502, 2134705956413458

Offset

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..1000

T. Lu, The enumeration of trees with and without given limbs, Discr. Math., 154 (1996), 153-165, Example 4.

Index entries for sequences related to trees

Formula

G.f. (x-2*x^3+x^4)/[Product_{p >= 1} (1-x^p)^(2*a(p))], in implicit form. - R. J. Mathar, Feb 26 2016

a(n) ~ c * d^n / n^(3/2), where d = 5.31351404806511900111976949727598017431010423107784202438023676025442... and c = 0.19638268380963259854038594083610578852611575... . - Vaclav Kotesovec, Feb 28 2016

Mathematica

nmax = 30; b = ConstantArray[0, nmax+1]; b[[1]] = 0; b[[2]] = 1; Do[b[[n+1]] = SeriesCoefficient[(x - 2*x^3 + x^4) / Product[(1 - x^p)^(2*b[[p+1]]), {p, 1, n-1}], {x, 0, n}], {n, 2, nmax}]; b (* Vaclav Kotesovec, Feb 28 2016 *)

Crossrefs

Sequence in context: A148436 A148437 A106873 * A255541 A150026 A150027

Adjacent sequences: A014270 A014271 A014272 * A014274 A014275 A014276

Keyword

nonn

Author

N. J. A. Sloane.

Status

approved