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A030699 Maximal value of Q(n,m) (number of partitions of n into m distinct summands) for given n. 6
1, 1, 1, 1, 2, 2, 3, 3, 4, 4, 5, 7, 8, 10, 12, 14, 16, 19, 21, 24, 27, 34, 39, 47, 54, 64, 72, 84, 94, 108, 120, 136, 150, 169, 192, 221, 255, 291, 333, 377, 427, 480, 540, 603, 674, 748, 831, 918, 1014, 1115, 1226, 1360, 1540, 1729, 1945, 2172, 2432, 2702, 3009 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

REFERENCES

L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 115.

LINKS

T. D. Noe and Gheorghe Coserea, Table of n, a(n) for n = 1..10000 (first 1000 terms from T. D. Noe)

A. Comtet, S. N. Majumdar and S. Ouvry, Integer Partitions and Exclusion Statistics, arXiv:0705.2640 [cond-mat.stat-mech], 2007

FORMULA

a(n) = max {Q(n,k), k=1..m}, where m = A003056(n) and Q(n,k) is defined by A008289. - Gheorghe Coserea, Nov 04 2015

a(n) ~ K * exp(Pi*sqrt(n/3)) / n, where K = Pi / (4*sqrt(6*Pi^2 - 72*log(2)^2)) = 0.158271121170... (see A260061). - Gheorghe Coserea, Nov 08 2015

MATHEMATICA

Max /@ Table[Length@ Select[IntegerPartitions[n, m], Sort@ DeleteDuplicates@ # == Range@ m &], {n, 32}, {m, 0, n}] (* Michael De Vlieger, Nov 06 2015 *)

PROG

(PARI)

Q(N) = {

  my(q = vector(N)); q[1] = [1, 0, 0, 0];

  for (n = 2, N,

    my(m = (sqrtint(8*n+1) - 1)\2);

    q[n] = vector((1 + (m>>2)) << 2); q[n][1] = 1;

    for (k = 2, m, q[n][k] = q[n-k][k] + q[n-k][k-1]));

  return(q);

};

apply(vecmax, Q(59))  \\ Gheorghe Coserea, Nov 04 2015

CROSSREFS

Cf. A003056, A008289, A257639, A260061.

Sequence in context: A035448 A060969 A152162 * A083802 A198318 A100881

Adjacent sequences:  A030696 A030697 A030698 * A030700 A030701 A030702

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from David Wasserman, Jan 23 2002

STATUS

approved

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Last modified March 21 04:59 EDT 2019. Contains 321364 sequences. (Running on oeis4.)