A241341 - OEIS

%I #11 Apr 26 2014 21:13:08

%S 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,

%T 384,422,481,751,624,1149,1142,1558,2096,2120,2116,3748,4477,5075,

%U 4788,7840,7543,11227,11772,13122,18916,22408,19619,29862,32604,41688

%N Number of partitions p of n such that ceiling(mean(p)) is a part and floor(mean(p)) is not.

%e a(10) counts these 4 partitions:  541, 5311, 442, 3331.

%t z = 30; f[n_] := f[n] = IntegerPartitions[n];

%t     t1 = Table[Count[f[n], p_ /; MemberQ[p, Floor[Mean[p]]] && MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241340 *)

%t     t2 = Table[Count[f[n], p_ /; ! MemberQ[p, Floor[Mean[p]]] && MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241341 *)

%t     t3 = Table[Count[f[n], p_ /; MemberQ[p, Floor[Mean[p]]] && ! MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241342 *)

%t     t4 = Table[Count[f[n], p_ /; ! MemberQ[p, Floor[Mean[p]]] && ! MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241343 *)

%t     t5 = Table[Count[f[n], p_ /; MemberQ[p, Floor[Mean[p]]] || MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241344 *)

%Y Cf. A241340, A241342, A241343, A241344.

%K nonn,easy

%O 0,11

%A _Clark Kimberling_, Apr 20 2014