A237822 Number of partitions of n such that (greatest part) + (least part) < number of parts.

0, 0, 1, 1, 2, 3, 5, 6, 10, 14, 19, 26, 36, 47, 64, 84, 110, 142, 185, 236, 304, 384, 486, 612, 769, 957, 1193, 1477, 1826, 2247, 2761, 3373, 4122, 5014, 6089, 7372, 8909, 10731, 12913, 15493, 18559, 22178, 26464, 31504, 37458, 44440, 52648, 62260, 73526

Offset

1,5

Links

Table of n, a(n) for n=1..49.

Example

a(6) = 3 counts these partitions:  2211, 2111, 111111.

Mathematica

z = 60; q[n_] := q[n] = IntegerPartitions[n]; t[p_] := t[p] = Length[p];
Table[Count[q[n], p_ /; Max[p] + Min[p] < t[p]], {n, z}]  (* A237822 *)
Table[Count[q[n], p_ /; Max[p] + Min[p] <= t[p]], {n, z}] (* A237823 *)
Table[Count[q[n], p_ /; Max[p] + Min[p] == t[p]], {n, z}] (* A237869 *)
Table[Count[q[n], p_ /; Max[p] + Min[p] > t[p]], {n, z}]  (* A237870 *)
Table[Count[q[n], p_ /; Max[p] + Min[p] >= t[p]], {n, z}] (* A237871 *)
Table[Count[IntegerPartitions[n], _?(#[[1]]+#[[-1]]<Length[#]&)], {n, 50}] (* Harvey P. Dale, Jul 26 2022 *)

Crossrefs

Cf. A237823, A237869-A237871.

Sequence in context: A131627 A325712 A345170 * A325713 A325714 A325715

Adjacent sequences: A237819 A237820 A237821 * A237823 A237824 A237825

Keyword

nonn,easy

Author

Clark Kimberling, Feb 18 2014

Status

approved