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%I A237758 #9 Feb 22 2014 13:17:43
%S A237758 0,0,1,2,4,6,10,14,21,30,42,58,80,108,144,192,252,329,426,549,702,895,
%T A237758 1131,1427,1789,2237,2781,3450,4259,5247,6436,7878,9607,11693,14182,
%U A237758 17172,20727,24974,30008,35997,43072,51457,61330,72988,86677,102785,121645
%N A237758 Number of partitions of n such that 2*(least part) < number of parts.
%e A237758 a(5) = 4 counts these partitions: 311, 221, 2111, 11111.
%t A237758 z = 55; q[n_] := q[n] = IntegerPartitions[n]; t[p_] := Length[p];
%t A237758 Table[Count[q[n], p_ /; 2 Min[p] < t[p]], {n, z}]   (* A237758 *)
%t A237758 Table[Count[q[n], p_ /; 2 Min[p] <= t[p]], {n, z}]  (* A118084 *)
%t A237758 Table[Count[q[n], p_ /; 2 Min[p] == t[p]], {n, z}]  (* A237757 *)
%t A237758 Table[Count[q[n], p_ /; 2 Min[p] > t[p]], {n, z}]   (* A237799 *)
%t A237758 Table[Count[q[n], p_ /; 2 Min[p] >= t[p]], {n, z}]  (* A237800 *)
%Y A237758 Cf. A118084, A237757, A237799, A237800.
%K A237758 nonn,easy
%O A237758 1,4
%A A237758 _Clark Kimberling_, Feb 15 2014

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