login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A136564 Array read by rows: T(n,k) is the number of directed multigraphs with loops with n arcs, k vertices, and no vertex of degree 0. 6
1, 1, 1, 5, 4, 1, 1, 9, 21, 16, 4, 1, 1, 18, 71, 108, 71, 22, 4, 1, 1, 27, 194, 491, 557, 326, 101, 22, 4, 1, 1, 43, 476, 1903, 3353, 3062, 1587, 497, 111, 22, 4, 1, 1, 59, 1030, 6298, 16644, 22352, 17035, 7982, 2433, 555, 111, 22, 4, 1, 1, 84, 2095, 18823, 72064 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Length of the n^th row: 2n.

LINKS

Table of n, a(n) for n=1..61.

FORMULA

T(n,1) = 1 if n > 0.

T(n,2n) = 1 if n > 0.

T(n,2n-1) = 4 if n >= 2.

T(n,2n-k) = A144047(k) for n large enough (conjecturally, n >= 2k is enough).

T(n,2) = (n^3 + 6*n^2 + 11*n - 6)/12 + ((n+2)/4)[n even]. (the bracket means that the second term is added if and only if n is even). - Benoit Jubin, Mar 31 2012

EXAMPLE

1, 1;

1, 5, 4, 1;

1, 9, 21, 16, 4, 1;

1, 18, 71, 108, 71, 22, 4, 1;

1, 27, 194, 491, 557, 326, 101, 22, 4, 1;

1, 43, 476, 1903, 3353, 3062, 1587, 497, 111, 22, 4, 1;

1, 59, 1030, 6298, 16644, 22352, 17035, 7982, 2433, 555, 111, 22, 4, 1;

CROSSREFS

Row sums: A052171. Partial row sums: A138107.

Sums of the first m entries of each row: A005993 (m=2), A050927 (m=3), A050929 (m=4).

Sequence in context: A213658 A046575 A154739 * A136042 A268911 A166044

Adjacent sequences:  A136561 A136562 A136563 * A136565 A136566 A136567

KEYWORD

nonn,tabf

AUTHOR

Benoit Jubin, Apr 14 2008

EXTENSIONS

More terms from Benoit Jubin and Vladeta Jovovic, Sep 08 2008

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 14 19:12 EST 2018. Contains 317214 sequences. (Running on oeis4.)