A147877 The number of degree sequences with degree sum 2n representable by a non-separable graph (with multiple edges allowed).

1, 1, 2, 3, 5, 9, 15, 25, 43, 70, 113, 181, 283, 436, 666, 999, 1483, 2179, 3166, 4556, 6504, 9200, 12918, 18011, 24938, 34308, 46928, 63815, 86324, 116187, 155626, 207502, 275491, 364226, 479660, 629305, 822655, 1071694, 1391531, 1801041, 2323958, 2989883

Offset

1,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 1..10000

O. J. Rodseth, J. A. Sellers and H. Tverberg, Enumeration of the Degree Sequences of Non-Separable Graphs and Connected Graphs, European Journal of Combinatorics 30 (2009), 1301-1317.

Formula

a(n) = p(2n) - p(2n-1) - Sum_{j=0..n-2} p(j).

a(n) = A000041(2*n) - A000041(2*n-1) - A000070(n) + A000041(n) + A000041(n-1). - Vaclav Kotesovec, Nov 05 2016

a(n) ~ exp(2*Pi*sqrt(n/3))*Pi/(48*n^(3/2)) * (1 - (3*sqrt(3)/(2*Pi) + 13*Pi/(48*sqrt(3)))/sqrt(n)). - Vaclav Kotesovec, Nov 05 2016

Maple

with(combinat): seq(numbpart(2*m) - numbpart(2*m - 1) - add(numbpart(j), j = 0 .. m-2), m=1..60);

Prog

(PARI) a(n) = numbpart(2*n) - numbpart(2*n-1) - sum(j=0, n-2, numbpart(j)); \\ Michel Marcus, Nov 04 2016

Crossrefs

Cf. A147878.

Sequence in context: A268709 A326024 A200047 * A003476 A017989 A017990

Adjacent sequences: A147874 A147875 A147876 * A147878 A147879 A147880

Keyword

nonn

Author

James A. Sellers, Nov 16 2008

Extensions

Offset corrected by Michel Marcus, Nov 04 2016

Status

approved