OFFSET
1,6
FORMULA
a(n) + a(n-1) = A002865(n) = A187219(n) = A085811(n+3), in all cases for n >= 2. - Omar E. Pol, Mar 07 2015
a(n) ~ exp(Pi*sqrt(2*n/3)) * Pi / (24*sqrt(2)*n^(3/2)). - Vaclav Kotesovec, Jun 02 2018
EXAMPLE
a(6) counts these 3 partitions: 33, 321, 222, of which the respective conjugates are 222, 321, 33.
MATHEMATICA
z = 53; f[n_] := f[n] = IntegerPartitions[n]; c[p_] := Table[Count[#, _?(# >= i &)], {i, First[#]}] &[p]; (* conjugate of partition p *)
Table[Count[f[n], p_ /; Count[p, 1] < Count[c[p], 1]], {n, 1, z}] (* A240690 *)
Table[Count[f[n], p_ /; Count[p, 1] <= Count[c[p], 1]], {n, 1, z}] (* A240690(n+1) *)
Table[Count[f[n], p_ /; Count[p, 1] == Count[c[p], 1]], {n, 1, z}] (* A240691 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 11 2014
STATUS
approved