STATUS
reviewed
approved
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Revision History for A029894
(Bold, blue-underlined text is an addition; faded, red-underlined text is aShowing entries 1-10 | older changes
Number of directed (or Gale-Ryser) graphical partitions: degree-vector pairs (in-degree, out-degree) for directed graphs (loops allowed) with n vertices; or possible ordered pair (row-sum, column-sum) vectors for a 0-1 matrix.
(history; published version)
(history; published version)
STATUS
proposed
reviewed
STATUS
editing
proposed
LINKS
Peter L. Erdos, I Miklós, Z Toroczkai, <a href="http://arxiv.org/abs/1601.08224">New classes of degree sequences with fast mixing swap Markov chain sampling</a>, arXiv preprint arXiv:1601.08224, [math.CO], 2016.
AUTHOR
TORSTENtorsten.SILLKEsillke(AT)LHSYSTEMSlhsystems.COMcom
STATUS
proposed
editing
STATUS
editing
proposed
FORMULA
a(n) = F(n, n, 0, n) where F(b, c, t, w) = Sum_{i=0..b} Sum_{j=ceiling((t+i)/w))..min(t+i, c)} F(i, j, t+i-j, w-1) for w > 0, F(b, c, 0, 0) = 1 and F(b, c, t, 0) = 0 for t > 0. - Andrew Howroyd, Nov 01 2019
PROG
(PARI) \\ see A327913 for T(n, m)
for(n=0, 15, print1(T(n, n), ", ")) \\ Andrew Howroyd, Nov 01 2019
LINKS
Andrew Howroyd, <a href="/A029894/b029894.txt">Table of n, a(n) for n = 0..30</a>
DATA
1, 2, 7, 34, 221, 1736, 15584, 153228, 1611189, 17826202, 205282376, 2441437708, 29816628471, 372314544202, 4737438631001, 61264426341926, 803488037899349, 10668478221202710, 143203795004873285, 1940953294927992976, 26536578116407809962, 365653739580163294032
KEYWORD
nonn,more,changed
EXTENSIONS
a(0)=1 prepended and terms a(12)-a() and beyond from Andrew Howroyd, Oct 31 2019
DATA
1, 2, 7, 34, 221, 1736, 15584, 153228, 1611189, 17826202, 205282376, 2441437708, 29816628471, 372314544202, 4737438631001, 61264426341926, 803488037899349, 10668478221202710
OFFSET
1,1
0,2
EXTENSIONS
a(0)=1 prepended and a(12)-a() from Andrew Howroyd, Oct 31 2019
STATUS
approved
editing
STATUS
editing
approved