A237869 Number of partitions of n such that (greatest part) + (least part) = number of parts.

0, 1, 0, 1, 1, 1, 1, 4, 2, 4, 5, 7, 8, 13, 12, 18, 22, 30, 33, 46, 51, 69, 81, 102, 120, 155, 179, 224, 265, 326, 383, 476, 553, 674, 793, 956, 1123, 1353, 1578, 1886, 2209, 2624, 3063, 3630, 4222, 4979, 5797, 6803, 7900, 9256, 10717, 12507, 14477, 16836

Offset

1,8

Links

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

Example

a(8) = 4 counts these partitions:  3311, 3221, 2222, 41111.

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 *)

Crossrefs

Cf. A237822, A237823, A237870, A237871.

Sequence in context: A167508 A167507 A007005 * A066978 A236187 A114566

Adjacent sequences: A237866 A237867 A237868 * A237870 A237871 A237872

Keyword

nonn,easy

Author

Clark Kimberling, Feb 18 2014

Status

approved