login
A241341
Number of partitions p of n such that ceiling(mean(p)) is a part and floor(mean(p)) is not.
5
0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 4, 6, 2, 13, 16, 14, 23, 41, 38, 73, 58, 94, 152, 196, 137, 271, 384, 422, 481, 751, 624, 1149, 1142, 1558, 2096, 2120, 2116, 3748, 4477, 5075, 4788, 7840, 7543, 11227, 11772, 13122, 18916, 22408, 19619, 29862, 32604, 41688
OFFSET
0,11
EXAMPLE
a(10) counts these 4 partitions: 541, 5311, 442, 3331.
MATHEMATICA
z = 30; f[n_] := f[n] = IntegerPartitions[n];
t1 = Table[Count[f[n], p_ /; MemberQ[p, Floor[Mean[p]]] && MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241340 *)
t2 = Table[Count[f[n], p_ /; ! MemberQ[p, Floor[Mean[p]]] && MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241341 *)
t3 = Table[Count[f[n], p_ /; MemberQ[p, Floor[Mean[p]]] && ! MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241342 *)
t4 = Table[Count[f[n], p_ /; ! MemberQ[p, Floor[Mean[p]]] && ! MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241343 *)
t5 = Table[Count[f[n], p_ /; MemberQ[p, Floor[Mean[p]]] || MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241344 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 20 2014
STATUS
approved