A241340 - OEIS

%I #7 Apr 26 2014 21:08:52

%S 0,1,2,3,4,5,7,8,11,15,18,22,37,36,50,73,89,100,152,161,249,290,330,

%T 413,646,666,803,1060,1348,1473,2170,2183,3003,3455,3984,5318,6936,

%U 6839,8494,10664,14064,14322,19343,20418,26417,32021,34068,40921,56205,57543

%N Number of partitions p of n such that floor(mean(p)) and ceiling(mean(p)) are parts of p.

%F a(n) + A241344(n) = A000041(n) for n >=1.

%e a(6) counts these 8 partitions:  6, 33, 321, 3111, 222, 2211, 21111, 111111.

%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. A241341, A241342, A241343, A241344.

%K nonn,easy

%O 0,3

%A _Clark Kimberling_, Apr 20 2014