A241322 - OEIS

%I #7 Jun 18 2015 04:00:36

%S 0,1,1,2,1,2,2,3,3,4,5,7,5,10,11,12,13,20,19,28,24,33,43,53,43,62,79,

%T 88,91,126,106,163,162,207,248,236,240,357,410,462,404,597,546,754,

%U 797,818,1080,1230,1077,1401,1491,1881,2051,2410,2284,2682,2701,3609

%N Number of partitions p of n into distinct parts, including floor(mean(p)) or ceiling(mean(p)).

%F a(n) + A241321(n) = A000009(n) for n >= 1.

%e a(11) counts these 7 partitions:  {11}, {7,3,1}, {6,5}, {6,4,1}, {6,3,2}, {5,4,2}, {5,3,2,1}.

%t z = 30; f[n_] := f[n] = Select[IntegerPartitions[n], Max[Length /@ Split@#] == 1 &];

%t     Table[Count[f[n], p_ /; MemberQ[p, Floor[Mean[p]]] && MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241318 *)

%t     Table[Count[f[n], p_ /; ! MemberQ[p, Floor[Mean[p]]] && MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241319 *)

%t     Table[Count[f[n], p_ /; MemberQ[p, Floor[Mean[p]]] && ! MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241320 *)

%t     Table[Count[f[n], p_ /; ! MemberQ[p, Floor[Mean[p]]] && ! MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241321 *)

%t     Table[Count[f[n], p_ /; MemberQ[p, Floor[Mean[p]]] || MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241322 *)

%Y Cf. A241318, A241319, A241320, A241321, A241312, A000009.

%K nonn,easy

%O 0,4

%A _Clark Kimberling_, Apr 19 2014