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 A053534 Triangle T(n,k) giving number of pairwise non-isomorphic (i.e., unlabeled) matroids of rank k on n points (n >= 0, 0 <= k <= n). 5
 1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 7, 4, 1, 1, 5, 13, 13, 5, 1, 1, 6, 23, 38, 23, 6, 1, 1, 7, 37, 108, 108, 37, 7, 1, 1, 8, 58, 325, 940, 325, 58, 8, 1, 1, 9, 87, 1275, 190214, 190214, 1275, 87, 9, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 LINKS W. M. B. Dukes, Tables of matroids. W. M. B. Dukes, Counting and Probability in Matroid Theory, Ph.D. Thesis, Trinity College, Dublin, 2000. W. M. B. Dukes, The number of matroids on a finite set, arXiv:math/0411557 [math.CO], 2004. W. M. B. Dukes, On the number of matroids on a finite set, SÃ©minaire Lotharingien de Combinatoire 51 (2004), Article B51g. Dillon Mayhew and Gordon F. Royle, Matroids with nine elements, arXiv:math/0702316 [math.CO], 2007 (see p. 7). Dillon Mayhew and Gordon F. Royle, Matroids with nine elements, J. Combin. Theory Ser. B 98(2) (2008), 415-431. FORMULA From Petros Hadjicostas, Oct 10 2019: (Start) T(n,0) = 1 for n >= 0. T(n,1) = n for n >= 1. T(n,2) = -n + Sum_{k = 1..n} p(k) for n >= 2, where p(k) = A000041(k). [Dukes (2004), Theorem 2.1.] (End) EXAMPLE The triangle, transposed, begins: k...n=0...n=1...n=2...n=3...n=4...n=5...n=6...n=7...n=8...n=9... 0.|.1.....1.....1.....1.....1.....1.....1.....1.....1.......1..... 1.|.......1.....2.....3.....4.....5.....6.....7.....8.......9..... 2.|.............1.....3.....7....13....23....37....58......87..... 3.|...................1.....4....13....38...108...325....1275..... 4.|.........................1.....5....23...108...940..190214..... 5.|...............................1.....6....37...325..190214..... 6.|.....................................1.....7....58....1275..... 7.|...........................................1.....8......87..... 8.|.................................................1.......9..... 9.|.........................................................1..... Sum.1.....2.....4.....8....17....38....98...306..1724..383172 CROSSREFS Row sums give A055545. Columns include (truncated versions of) A000012 (k=0), A000027 (k=1), A058682 (k=2), A058693 (k=3). Cf. A000041, A058669. Sequence in context: A088699 A101515 A028657 * A104881 A171699 A104878 Adjacent sequences:  A053531 A053532 A053533 * A053535 A053536 A053537 KEYWORD nonn,tabl,nice,changed AUTHOR N. J. A. Sloane, Dec 30 2000 EXTENSIONS More terms from Jonathan Vos Post, Feb 14 2007 Edited by N. J. A. Sloane, Jul 03 2008 at the suggestion of R. J. Mathar and Max Alekseyev STATUS approved

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Last modified October 22 22:34 EDT 2019. Contains 328335 sequences. (Running on oeis4.)