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A237822
Number of partitions of n such that (greatest part) + (least part) < number of parts.
5
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
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
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Feb 18 2014
STATUS
approved