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A147878 The number of degree sequences with degree sum 2n representable by a connected graph (with multiple edges allowed). 18
1, 2, 5, 11, 23, 46, 86, 156, 273, 463, 766, 1241, 1969, 3073, 4723, 7157, 10711, 15850, 23206, 33654, 48373, 68955, 97544, 137002, 191125, 264955, 365127, 500349, 682018, 924982, 1248502, 1677530, 2244229, 2989952, 3967732, 5245354, 6909211 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
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(n-1) - 2*Sum_{j=0..n-2} p(j).
a(n) = A000041(2*n) - 2*A000070(n) + 2*A000041(n) + A000041(n-1). - Vaclav Kotesovec, Nov 05 2016
a(n) ~ exp(2*Pi*sqrt(n/3))/(8*sqrt(3)*n) * (1 - (sqrt(3)/(2*Pi) + Pi/(48*sqrt(3))) /sqrt(n)). - Vaclav Kotesovec, Nov 05 2016
EXAMPLE
From Gus Wiseman, Oct 26 2018: (Start)
The a(1) = 1 through a(5) = 23 connected multigraphical partitions:
(11) (22) (33) (44) (55)
(211) (222) (332) (433)
(321) (422) (442)
(2211) (431) (532)
(3111) (2222) (541)
(3221) (3322)
(3311) (3331)
(4211) (4222)
(22211) (4321)
(32111) (4411)
(41111) (5221)
(5311)
(22222)
(32221)
(33211)
(42211)
(43111)
(52111)
(222211)
(322111)
(331111)
(421111)
(511111)
(End)
MAPLE
with(combinat): seq(numbpart(2*m) - numbpart(m - 1) - 2*add(numbpart(j), j = 0 .. m-2), m=1..60);
PROG
(PARI) a(n) = numbpart(2*n) - numbpart(n-1) - 2*sum(j=0, n-2, numbpart(j)); \\ Michel Marcus, Nov 04 2016
CROSSREFS
Sequence in context: A005986 A333396 A277828 * A179902 A140992 A248646
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 May 18 08:45 EDT 2024. Contains 372618 sequences. (Running on oeis4.)