OFFSET
1,5
COMMENTS
LINKS
Gheorghe Coserea, Table of n, a(n) for n = 1..50000
Paul Erdős, On some asymptotic formulas in the theory of partitions, Bull. Amer. Math. Soc. 52 (1946), no. 2, 185--188.
B. Richmond and A. Knopfmacher, Compositions with distinct parts, Aequationes Mathematicae 49 (1995), pp. 86-97.
G. Szekeres, Some asymptotic formulas in the theory of partitions (II), Quart. J. Math. Oxford (2), 4(1953), 96-111.
FORMULA
EXAMPLE
For n=9, a(9)=2 because A003056(9)=3 and max{Q(9,p), p=1..3}=4 and Q(9,2)=4.
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);
};
seq(N) = {
my(a = vector(N), q = Q(N), vmx = apply(vecmax, q));
for (n = 1, N, a[n] = vecmin(select(v->v==vmx[n], q[n], 1)));
a;
};
seq(86) \\ updated by Gheorghe Coserea, Jun 02 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Gheorghe Coserea, Nov 04 2015
STATUS
approved