A143841 - OEIS

A143841

Table read by antidiagonals: T(n,k) is the number of strongly connected directed multigraphs with loops with n arcs and up to k vertices.

1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 2, 1, 0, 1, 1, 2, 3, 1, 0, 1, 1, 2, 4, 7, 1, 0, 1, 1, 2, 4, 11, 11, 1, 0, 1, 1, 2, 4, 12, 30, 20, 1, 0, 1, 1, 2, 4, 12, 36, 93, 29, 1, 0, 1, 1, 2, 4, 12, 37, 152, 237, 45, 1, 0, 1, 1, 2, 4, 12, 37, 161, 587, 579, 61, 1, 0

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

0,13

LINKS

Andrew Howroyd, Table of n, a(n) for n = 0..860

FORMULA

T(n,k) = Sum_{p=0..k} A139622(n,p).

T(n,k) = A139627(n) for k >= n.

T(n,2) = A129620(n,2) - n*(n-1)/2.

EXAMPLE

Array begins:

=============================================

n\k | 0 1 2 3 4 5 6 7 8

----+----------------------------------------

0 | 1 1 1 1 1 1 1 1 1 ...

1 | 0 1 1 1 1 1 1 1 1 ...

2 | 0 1 2 2 2 2 2 2 2 ...

3 | 0 1 3 4 4 4 4 4 4 ...

4 | 0 1 7 11 12 12 12 12 12 ...

5 | 0 1 11 30 36 37 37 37 37 ...

6 | 0 1 20 93 152 161 162 162 162 ...

7 | 0 1 29 237 587 725 737 738 738 ...

8 | 0 1 45 579 2249 3610 3911 3927 3928 ...

...

PROG

(PARI) \\ See PARI link in A350489 for program code.

A(n)={my(data=A139622rows(n), M=matrix(n+1, n+1, i, j, if(i==1, 1, sum(k=1, min(i-1, j-1), data[i-1][k])))); M}

{ my(M=A(8)); for(n=1, #M~, print(M[n, ])) } \\ Andrew Howroyd, Jan 14 2022

CROSSREFS

Partial sums of the rows of A139622.

Main diagonal is A139627.

Cf. A138107, A129620, A143842, A350489.

Sequence in context: A262553 A247506 A182172 * A276719 A276837 A269941

Adjacent sequences: A143838 A143839 A143840 * A143842 A143843 A143844

KEYWORD

nonn,tabl

AUTHOR

Benoit Jubin, Sep 02 2008

EXTENSIONS

Name clarified and terms a(32) and beyond from Andrew Howroyd, Jan 14 2022

STATUS

approved