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A007721 Number of distinct degree sequences among all connected graphs with n nodes. 4


%S 1,1,2,6,19,68,236,863,3137,11636,43306,162728,614142,2330454,8875656,

%T 33924699,130038017,499753560,1924912505,7429159770,28723877046,

%U 111236422377,431403469046,1675316533812,6513837677642,25354842098354,98794053266471,385312558567775

%N Number of distinct degree sequences among all connected graphs with n nodes.

%C Sometimes called "graphical partitions", although this term is deprecated.

%H Wang Kai, <a href="/A007721/b007721.txt">Table of n, a(n) for n = 1..118</a>

%H N. Durand, G. Granger, <a href="http://atm2003.eurocontrol.fr/past-seminars/5th-seminar-budapest-hungary-june-2003/papers/paper_033/view">A traffic complexity approach through cluster analysis</a>, in proceedings of the 5th ATM R&D Seminar, Budapest, Hungary (2003)

%H T. Hoppe, A. Petrone,<a href="http://arxiv.org/abs/1408.3644">Integer sequence discovery from small graphs</a>, arXiv preprint arXiv:1408.3644 [math.CO], 2014.

%H F. Ruskey, <a href="http://webhome.cs.uvic.ca/~ruskey/Publications/AlleyCat/AlleyCat.html">Alley CATs in search of good homes</a>, Congress. Numerant., 102 (1994) 97-110.

%H Kai Wang, <a href="https://arxiv.org/abs/1604.04148">Efficient Counting of Degree Sequences</a>, arXiv preprint arXiv:1604.04148 [math.CO], 2017.

%H <a href="/index/Gra#graph_part">Index entries for sequences related to graphical partitions</a>

%Y Cf. A000569, A004250, A004251, A007722, A029889; A095268 (analog for all graphs).

%K nonn,nice

%O 1,3

%A _Frank Ruskey_

%E a(9) corrected by _Gordon Royle_, Aug 30 2006

%E More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), May 19 2007

%E Prepended missing term a(1), _Travis Hoppe_, Aug 04 2014

%E a(22)-a(28) added by _Wang Kai_, Feb 15 2017

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Last modified February 18 03:39 EST 2020. Contains 332006 sequences. (Running on oeis4.)