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A237800 Number of partitions of n such that 2*(least part) >= number of parts.

%I A237800 #7 Feb 22 2014 13:21:28
%S A237800 1,2,2,3,3,5,5,8,9,12,14,19,21,27,32,39,45,56,64,78,90,107,124,148,
%T A237800 169,199,229,268,306,357,406,471,536,617,701,805,910,1041,1177,1341,
%U A237800 1511,1717,1931,2187,2457,2773,3109,3503,3918,4403,4919,5514,6150,6881
%N A237800 Number of partitions of n such that 2*(least part) >= number of parts.
%e A237800 a(7) = 5 counts these partitions: 7, 61, 52, 43, 322.
%t A237800 z = 55; q[n_] := q[n] = IntegerPartitions[n]; t[p_] := Length[p];
%t A237800 Table[Count[q[n], p_ /; 2 Min[p] < t[p]], {n, z}]   (* A237758 *)
%t A237800 Table[Count[q[n], p_ /; 2 Min[p] == t[p]], {n, z}]  (* A237757 *)
%t A237800 Table[Count[q[n], p_ /; 2 Min[p] > t[p]], {n, z}]   (* A237799 *)
%t A237800 Table[Count[q[n], p_ /; 2 Min[p] >= t[p]], {n, z}]  (* A237800 *)
%Y A237800 Cf. A237758, A118084, A237757, A237799.
%K A237800 nonn,easy
%O A237800 1,2
%A A237800 _Clark Kimberling_, Feb 15 2014