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

1, 2, 2, 3, 3, 5, 5, 8, 9, 12, 14, 19, 21, 27, 32, 39, 45, 56, 64, 78, 90, 107, 124, 148, 169, 199, 229, 268, 306, 357, 406, 471, 536, 617, 701, 805, 910, 1041, 1177, 1341, 1511, 1717, 1931, 2187, 2457, 2773, 3109, 3503, 3918, 4403, 4919, 5514, 6150, 6881

Offset

1,2

Links

Table of n, a(n) for n=1..54.

Example

a(7) = 5 counts these partitions: 7, 61, 52, 43, 322.

Mathematica

z = 55; q[n_] := q[n] = IntegerPartitions[n]; t[p_] := Length[p];
Table[Count[q[n], p_ /; 2 Min[p] < t[p]], {n, z}]   (* A237758 *)
Table[Count[q[n], p_ /; 2 Min[p] == t[p]], {n, z}]  (* A237757 *)
Table[Count[q[n], p_ /; 2 Min[p] > t[p]], {n, z}]   (* A237799 *)
Table[Count[q[n], p_ /; 2 Min[p] >= t[p]], {n, z}]  (* A237800 *)

Crossrefs

Cf. A237758, A118084, A237757, A237799.

Sequence in context: A371794 A239949 A103609 * A232697 A129526 A246998

Adjacent sequences: A237797 A237798 A237799 * A237801 A237802 A237803

Keyword

nonn,easy

Author

Clark Kimberling, Feb 15 2014

Status

approved