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A058716 Triangle T(n,k) giving number of nonisomorphic loopless matroids of rank k on n labeled points (n >= 0, 0<=k<=n). 6
1, 0, 1, 0, 1, 1, 0, 1, 2, 1, 0, 1, 4, 3, 1, 0, 1, 6, 9, 4, 1, 0, 1, 8, 19, 16, 5, 1, 0, 1, 10, 33, 44, 25, 6, 1, 0, 1, 12, 51, 96, 85, 36, 7, 1, 0, 1, 14, 73, 180, 225, 146, 49, 8, 1, 0, 1, 16, 99, 304, 501, 456, 231, 64, 9, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,9

COMMENTS

A signed version is given by A119328. - Paul Barry, May 14 2006

LINKS

Table of n, a(n) for n=0..65.

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

FORMULA

T(n,k)=sum{i=0..n, (-1)^(i-k)*C(n,i)*sum{j=0..i-k, C(k,2j)*C(i-k,2j)}}; Column k has g.f. (x/(1-x))^k*sum{j=0..k, C(k,2j)x^(2j)}. - Paul Barry, May 14 2006

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, 0, n}] // Flatten (* Jean-François Alcover, Oct 21 2013 *)

CROSSREFS

Cf. A058717 (same except for border), A058710, A058711. Row sums give A058718. Diagonals give A000065, A058719.

Sequence in context: A055277 A055340 * A119328 A048723 A088455 A004248

Adjacent sequences:  A058713 A058714 A058715 * A058717 A058718 A058719

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

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Last modified February 22 21:45 EST 2018. Contains 299469 sequences. (Running on oeis4.)