A130131 Number of n-lobsters.

1, 1, 1, 2, 3, 6, 11, 23, 47, 105, 231, 532, 1224, 2872, 6739, 15955, 37776, 89779, 213381, 507949, 1209184, 2880382, 6861351, 16348887, 38955354, 92831577, 221219963, 527197861, 1256385522, 2994200524, 7135736613, 17005929485

Offset

1,4

Comments

A lobster graph is a tree having the property that the removal of all leaf nodes leaves a caterpillar graph (see A005418). - N. J. A. Sloane, Nov 05 2020

References

Wakhare, Tanay, Eric Wityk, and Charles R. Johnson. "The proportion of trees that are linear." Discrete Mathematics 343.10 (2020): 112008. Also arXiv:1901.08502v2. See Tables 1 and 2 (but beware errors).

Links

Andrew Howroyd, Table of n, a(n) for n = 1..200

Andrew Howroyd, Formula for number of lobsters

G. Li and F. Ruskey, C program

Eric Weisstein's World of Mathematics, Lobster Graph

Mathematica

eta = QPochhammer;
s[n_] := With[{ox = O[x]^n}, x^2 ((1/eta[x + ox] - 1/(1 - x))^2/(1 - x/eta[x + ox]) + (1/eta[x^2 + ox] - 1/(1 - x^2))(1 + x/eta[x + ox])/(1 - x^2/eta[x^2 + ox]))/2 + x/eta[x + ox] - x^3/((1 - x)^2*(1 + x))];
CoefficientList[s[32], x] // Rest (* Jean-François Alcover, Nov 17 2020, after Andrew Howroyd *)

Prog

(PARI)
s(n)={my(ox=O(x^n)); x^2*((1/eta(x+ox)-1/(1-x))^2/(1-x/eta(x+ox)) + (1/eta(x^2+ox)-1/(1-x^2))*(1+x/eta(x+ox))/(1-x^2/eta(x^2+ox)))/2 + x/eta(x+ox) - x^3/((1-x)^2*(1+x))}
Vec(s(30)) \\ Andrew Howroyd, Nov 02 2017

Crossrefs

Cf. A000055, A005418, A058984, A130132, A331693.

Sequence in context: A198655 A211694 A303586 * A338355 A277796 A123465

Adjacent sequences: A130128 A130129 A130130 * A130132 A130133 A130134

Keyword

nonn

Author

Eric W. Weisstein, May 11 2007

Extensions

a(15)-a(32) from Washington Bomfim, Feb 23 2011

Status

approved