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A138107 Infinite square array: T(n,k) = number of directed multigraphs with loops with n arcs and k vertices; read by falling antidiagonals. 10
1, 1, 0, 1, 1, 0, 1, 2, 1, 0, 1, 2, 6, 1, 0, 1, 2, 10, 10, 1, 0, 1, 2, 11, 31, 19, 1, 0, 1, 2, 11, 47, 90, 28, 1, 0, 1, 2, 11, 51, 198, 222, 44, 1, 0, 1, 2, 11, 52, 269, 713, 520, 60, 1, 0, 1, 2, 11, 52, 291, 1270, 2423, 1090, 85, 1, 0, 1, 2, 11, 52, 295, 1596, 5776, 7388, 2180, 110, 1, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,8

COMMENTS

Partial sums of the rows of A136564, i.e., T(n,k) = Sum_{p=0..k} A136564(n,p).

LINKS

Table of n, a(n) for n=0..77.

R. J. Mathar, Statistics on Small Graphs, arXiv:1709.09000 (2017) Table 79.

FORMULA

T(n,0) = A000007(n),

T(n,1) = A000012(n),

T(n,2) = A005993(n),

T(n,3) = A050927(n),

T(n,4) = A050929(n).

If k >= 2n, T(n,k) = A052171(n).

EXAMPLE

The array begins:

   1, 1,  1,    1,     1,     1,     1,     1,     1,...

   0, 1,  2,    2,     2,     2,     2,     2,     2,...

   0, 1,  6,   10,    11,    11,    11,    11,    11,...

   0, 1, 10,   31,    47,    51,    52,    52,    52,...

   0, 1, 19,   90,   198,   269,   291,   295,   296,  296...

   0, 1, 28,  222,   713,  1270,  1596,  1697,  1719, 1723...

   0, 1, 44,  520,  2423,  5776,  8838, 10425, 10922,...

   0, 1, 60, 1090,  7388, 24032, 46384, ...

   0, 1, 85, 2180, 21003, 93067, ..

   0, 1,110, 4090,...

   ...

CROSSREFS

Sequence in context: A138352 A129620 A074766 * A089631 A298878 A195982

Adjacent sequences:  A138104 A138105 A138106 * A138108 A138109 A138110

KEYWORD

nonn,tabl

AUTHOR

Benoit Jubin, May 03 2008

EXTENSIONS

More terms from Vladeta Jovovic and Benoit Jubin, Sep 10 2008

STATUS

approved

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Last modified February 20 02:07 EST 2018. Contains 299357 sequences. (Running on oeis4.)