A237799 Number of partitions of n such that 2*(least part) > number of parts.

1, 1, 1, 2, 2, 4, 4, 6, 7, 9, 10, 14, 15, 19, 23, 28, 32, 40, 46, 56, 65, 77, 89, 107, 122, 143, 165, 193, 220, 257, 292, 338, 385, 443, 503, 578, 653, 746, 844, 962, 1083, 1231, 1384, 1567, 1761, 1987, 2227, 2510, 2807, 3153, 3523, 3949, 4403, 4927, 5485

Offset

1,4

Links

Table of n, a(n) for n=1..55.

Example

a(7) = 4 counts these partitions: 7, 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, A237800.

Sequence in context: A319400 A174787 A094909 * A318029 A319401 A322369

Adjacent sequences: A237796 A237797 A237798 * A237800 A237801 A237802

Keyword

nonn,easy

Author

Clark Kimberling, Feb 15 2014

Status

approved