%I #18 Nov 05 2016 05:18:01

%S 1,1,2,3,5,9,15,25,43,70,113,181,283,436,666,999,1483,2179,3166,4556,

%T 6504,9200,12918,18011,24938,34308,46928,63815,86324,116187,155626,

%U 207502,275491,364226,479660,629305,822655,1071694,1391531,1801041,2323958,2989883

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

%H Vaclav Kotesovec, <a href="/A147877/b147877.txt">Table of n, a(n) for n = 1..10000</a>

%H O. J. Rodseth, J. A. Sellers and H. Tverberg, <a href="http://dx.doi.org/10.1016/j.ejc.2008.10.006">Enumeration of the Degree Sequences of Non-Separable Graphs and Connected Graphs</a>, European Journal of Combinatorics 30 (2009), 1301-1317.

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

%F a(n) = A000041(2*n) - A000041(2*n-1) - A000070(n) + A000041(n) + A000041(n-1). - _Vaclav Kotesovec_, Nov 05 2016

%F 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

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

%o (PARI) a(n) = numbpart(2*n) - numbpart(2*n-1) - sum(j=0, n-2, numbpart(j)); \\ _Michel Marcus_, Nov 04 2016

%Y Cf. A147878.

%K nonn

%O 1,3

%A _James A. Sellers_, Nov 16 2008

%E Offset corrected by _Michel Marcus_, Nov 04 2016