A237820 Number of partitions of n such that 2*(least part) < greatest part.

0, 0, 0, 1, 2, 4, 8, 12, 19, 29, 42, 58, 83, 112, 151, 202, 267, 347, 453, 581, 744, 948, 1198, 1505, 1889, 2356, 2925, 3621, 4465, 5486, 6724, 8212, 9999, 12151, 14715, 17784, 21442, 25795, 30952, 37079, 44315, 52871, 62950, 74827, 88767, 105159, 124335

Offset

1,5

Links

Table of n, a(n) for n=1..47.

Example

a(6) = 4 counts these partitions:  51, 411, 321, 3111.

Mathematica

z = 60; q[n_] := q[n] = IntegerPartitions[n];
Table[Count[q[n], p_ /; 2 Min[p] < Max[p]], {n, z}]  (* A237820 *)
Table[Count[q[n], p_ /; 2 Min[p] <= Max[p]], {n, z}] (* A237821 *)
Table[Count[q[n], p_ /; 2 Min[p] = = Max[p]], {n, z}](* A118096 *)
Table[Count[q[n], p_ /; 2 Min[p] > Max[p]], {n, z}]  (* A053263 *)
Table[Count[q[n], p_ /; 2 Min[p] >= Max[p]], {n, z}] (* A237824 *)

Crossrefs

Cf. A237821, A118096, A053263, A237824.

Sequence in context: A011908 A117455 A277753 * A110571 A037168 A049696

Adjacent sequences: A237817 A237818 A237819 * A237821 A237822 A237823

Keyword

nonn,easy

Author

Clark Kimberling, Feb 16 2014

Status

approved