cp's OEIS Frontend

A240180 Number of partitions of n such that (least part) = (multiplicity of greatest part).

%I A240180 #8 Apr 28 2014 15:02:35
%S A240180 0,1,0,1,3,3,5,7,12,16,24,30,45,57,81,104,143,179,243,304,399,504,650,
%T A240180 809,1039,1286,1622,2006,2508,3077,3822,4666,5747,6995,8552,10353,
%U A240180 12603,15189,18371,22071,26570,31785,38104,45419,54213,64426,76596,90710
%N A240180 Number of partitions of n such that (least part) = (multiplicity of greatest part).
%C A240180 Also the number of partitions p of n such that min(p) = min(conjugate(p)). Example:a(7) counts these 7 partitions:  61, 511, 421, 4111, 3211, 31111, 211111, of which the respective conjugates are 211111, 31111, 3211, 4111, 421, 511, 61. - _Clark Kimberling_, Apr 11 2014
%F A240180 a(n) = A240179(n) - A240178(n), for n >= 0.
%F A240180 a(n) + 2*A240178(n) = A000041(n) for n >= 0.
%e A240180 a(6) counts these 5 partitions:  51, 411, 321, 3111, 21111.
%t A240180 z = 60; f[n_] := f[n] = IntegerPartitions[n];
%t A240180 Table[Count[f[n], p_ /; Min[p] < Count[p, Max[p]]], {n, 0, z}]  (* A240178 *)
%t A240180 Table[Count[f[n], p_ /; Min[p] <= Count[p, Max[p]]], {n, 0, z}] (* A240179 *)
%t A240180 Table[Count[f[n], p_ /; Min[p] == Count[p, Max[p]]], {n, 0, z}] (* A240180 *)
%t A240180 Table[Count[f[n], p_ /; Min[p] > Count[p, Max[p]]], {n, 0, z}]  (* A240178, n>0 *)
%t A240180 Table[Count[f[n], p_ /; Min[p] >= Count[p, Max[p]]], {n, 0, z}] (* A240179, n>0 *)
%Y A240180 Cf. A240178, A240179, A000041.
%K A240180 nonn,easy
%O A240180 0,5
%A A240180 _Clark Kimberling_, Apr 02 2014