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A147877 The number of degree sequences with degree sum 2n representable by a non-separable graph (with multiple edges allowed). 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
LINKS
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
KEYWORD
nonn
AUTHOR
James A. Sellers, Nov 16 2008
EXTENSIONS
Offset corrected by Michel Marcus, Nov 04 2016
STATUS
approved

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Last modified March 19 04:58 EDT 2024. Contains 370952 sequences. (Running on oeis4.)