OFFSET
1,2
COMMENTS
a(n) is also the number of partitions of n with a part whose multiplicity is greater than half the total number of parts. - Andrew Howroyd, Jan 17 2024
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 1..10000 (using data from A238589)
FORMULA
a(n) ~ Pi * exp(Pi*sqrt(2*n/3)) / (3*2^(3/2)*n^(3/2)). - Vaclav Kotesovec, Jun 09 2021
a(n) = Sum_{k>=1} x^(2*k-2)*(1 + x - x^(k-1))/(Product_{j=1..k} (1 - x^j)). - Andrew Howroyd, Jan 17 2024
EXAMPLE
a(6) counts all 11 partitions of 6 except these: 42, 321, 2211, 21111.
MATHEMATICA
Table[Count[IntegerPartitions[n], p_ /; !MemberQ[p, 2*Min[p]]], {n, 50}]
PROG
(PARI) seq(n) = {Vec(sum(k=1, n\2+1, x^(2*k-2)*(1 + x - x^(k-1))/prod(j=1, k, 1 - x^j, 1 + O(x^(n-2*k+3))), O(x*x^n)))} \\ Andrew Howroyd, Jan 17 2024
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Mar 01 2014
STATUS
approved