login
A241740
Number of partitions p of n such that (number of numbers in p of form 3k+2) < (number of numbers in p of form 3k).
9
0, 0, 0, 1, 1, 1, 3, 4, 4, 7, 10, 12, 17, 24, 30, 40, 53, 70, 90, 118, 152, 194, 244, 316, 396, 497, 626, 784, 960, 1202, 1483, 1816, 2230, 2738, 3312, 4042, 4908, 5922, 7141, 8627, 10327, 12388, 14832, 17703, 21075, 25120, 29795, 35321, 41822, 49439, 58286
OFFSET
0,7
COMMENTS
Each number in p is counted once, regardless of its multiplicity.
FORMULA
a(n) + A241741(n) + A241842(n) = A000041(n) for n >= 0.
EXAMPLE
a(8) counts these 4 partitions: 611, 431, 3311, 311111.
MATHEMATICA
z = 40; f[n_] := f[n] = IntegerPartitions[n]; s[k_, p_] := Count[Mod[DeleteDuplicates[p], 3], k];
Table[Count[f[n], p_ /; s[2, p] < s[0, p]], {n, 0, z}] (* A241740 *)
Table[Count[f[n], p_ /; s[2, p] == s[0, p]], {n, 0, z}] (* A241741 *)
Table[Count[f[n], p_ /; s[2, p] > s[0, p]], {n, 0, z}] (* A241742 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 28 2014
STATUS
approved