editing

proposed

Michel Marcus: data setion is too big: I think should stop after 1, 2, 5, 9, 13

William P. Orrick: Michel Marcus, you are right. I will take this back to editing until that, and a few outer mistakes, are corrected.

Martin Aigner, <a href="https://archive.org/details/markovstheorem100000aign.html">Markov's theorem and 100 years of the uniqueness conjecture. A mathematical journey from irrational numbers to perfect matchings</a>, [archive.org copy of the book].

~~~ ".html" added to link.

Wouter Meeussen: I advise to lift W. Orrick's editting and submission limitations. His work is very good.

proposed

reviewed

editing

proposed

~~~ _Wouter Meeussen_, Jan 16 2024 Conjecture: count of even Markov numbers in generation n (with generations 0, 1 and 2 labeled as {5} , {13, 29} and {34, 194, 433, 169}. (Checked up to generation 20).

~~~ _Wouter Meeussen_, Jan 16 2024 Markov conjecture added.

~~~ Conjecture: count of even Markov numbers in generation n (with generations 0, 1 and 2 labeled as {5} , {13, 29} and {34, 194, 433, 169}. (Checked up to generation 20).

Cf. A002487.; A002559

Entries checked by Zak Seidov, Oct 26 2006;

~~~ Markov conjecture added.

approved

editing

Table[PartitionsP[n]-(1 + Floor[n^2/4]), {n, 0, 30}];

Table[ Count[Partitions[n], pa_ /; Length[DeleteCases[pa, 1]] > 2] , {n, , 0, 30}]

Wouter Meeussen: now starting with offset 0, Mathematica formulae adapted.

proposed

editing

editing

proposed

0, 0, 0, 0, 0, 1, 2, 5, 9, 16, 25, 40, 58, 85, 119, 166, 224, 303, 399, 526, 681, 880, 1122, 1430, 1801, 2266, 2827, 3521, 4354, 5378, 6601, 8092, 9870, 12020, 14576, 17652, 21294, 25653, 30804, 36937, 44162, 52732, 62798, 74690, 88627, 105028, 124201, 146696, 172924, 203600, 239292, 280912

1,67

as requested by M. Marcus.

Wouter Meeussen: @Alois P. Heinz : well spotted! a leading zero escaped the copy-pasting. Corrected.