cp's OEIS Frontend

A238006 Number of strict partitions of n such that (greatest part) - (least part) > (number of parts).

%I A238006 #18 Sep 12 2021 14:12:47
%S A238006 0,0,0,0,1,1,2,3,5,6,8,11,14,18,22,27,33,41,49,59,70,83,98,116,136,
%T A238006 159,186,215,249,289,333,383,441,505,578,660,752,856,974,1105,1252,
%U A238006 1418,1602,1808,2039,2295,2581,2901,3255,3649,4088,4573,5111,5709,6368
%N A238006 Number of strict partitions of n such that (greatest part) - (least part) > (number of parts).
%F A238006 A001227(n) + A238005(n) + a(n) = A000009(n). - _R. J. Mathar_, Sep 08 2021
%F A238006 From _Omar E. Pol_, Sep 11 2021: (Start)
%F A238006 a(n) = A000009(n) - A003056(n).
%F A238006 a(n) = A238007(n) - A238005(n). (End)
%e A238006 a(8) = 3 counts these partitions:  7+1, 6+2, 5+2+1.
%t A238006 z = 70; q[n_] := q[n] = Select[IntegerPartitions[n], Max[Length /@ Split@#] == 1 &]; p1[p_] := p1[p] = DeleteDuplicates[p]; t[p_] := t[p] = Length[p1[p]];
%t A238006 Table[Count[q[n], p_ /; Max[p] - Min[p] < t[p]], {n, z}]  (* A001227 *)
%t A238006 Table[Count[q[n], p_ /; Max[p] - Min[p] <= t[p]], {n, z}] (* A003056 *)
%t A238006 Table[Count[q[n], p_ /; Max[p] - Min[p] == t[p]], {n, z}] (* A238005 *)
%t A238006 Table[Count[q[n], p_ /; Max[p] - Min[p] > t[p]], {n, z}]  (* A238006 *)
%t A238006 Table[Count[q[n], p_ /; Max[p] - Min[p] >= t[p]], {n, z}] (* A238007 *)
%Y A238006 Cf. A000009, A001227, A003056, A238005, A238007.
%K A238006 nonn,easy
%O A238006 1,7
%A A238006 _Clark Kimberling_, Feb 17 2014