login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A058717 Triangle T(n,k) giving number of nonisomorphic loopless matroids of rank k on n labeled points (n >= 1, 1<=k<=n). 1
1, 1, 1, 1, 2, 1, 1, 4, 3, 1, 1, 6, 9, 4, 1, 1, 8, 19, 16, 5, 1, 1, 10, 33, 44, 25, 6, 1, 1, 12, 51, 96, 85, 36, 7, 1, 1, 14, 73, 180, 225, 146, 49, 8, 1, 1, 16, 99, 304, 501, 456, 231, 64, 9, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

LINKS

Table of n, a(n) for n=1..55.

W. M. B. Dukes, Tables of matroids

W. M. B. Dukes, Counting and Probability in Matroid Theory, Ph.D. Thesis, Trinity College, Dublin, 2000.

Index entries for sequences related to matroids

W. M. B. Dukes, On the number of matroids on a finite set

EXAMPLE

1; 0,1; 0,1,1; 0,1,2,1; 0,1,4,3,1; ...

MATHEMATICA

t[n_, k_] := Sum[(-1)^(i-k)*Binomial[n, i]*Sum[Binomial[k, 2*j]*Binomial[i-k, 2*j], {j, 0, i-k}] , {i, 0, n}]; Table[t[n, k], {n, 0, 10}, {k, 1, n}] // Flatten (* Jean-François Alcover, Oct 21 2013 *)

CROSSREFS

Cf. A058716 (same except for border), A058710, A058711. Row sums give A058718. Diagonals give A000065, A058719.

Sequence in context: A161492 A177976 A034781 * A110470 A055080 A034367

Adjacent sequences:  A058714 A058715 A058716 * A058718 A058719 A058720

KEYWORD

nonn,tabl,nice

AUTHOR

N. J. A. Sloane, Dec 31 2000

EXTENSIONS

Corrected and extended by Jean-François Alcover, Oct 21 2013

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
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 20 19:02 EST 2020. Contains 332082 sequences. (Running on oeis4.)