OFFSET
1,6
LINKS
R. J. Mathar, Table of n, a(n) for n = 1..95
George E. Andrews, 4-Shadows in q-Series and the Kimberling Index, Preprint, May 15, 2016.
FORMULA
EXAMPLE
a(7) = 4 counts these partitions: 6+1, 5+2, 5+1+1, 4+2+1.
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}] (* A237830 *)
Table[Count[q[n], p_ /; Max[p] - Min[p] <= t[p]], {n, z}] (* A237831 *)
Table[Count[q[n], p_ /; Max[p] - Min[p] == t[p]], {n, z}] (* A237832 *)
Table[Count[q[n], p_ /; Max[p] - Min[p] > t[p]], {n, z}] (* A237833 *)
Table[Count[q[n], p_ /; Max[p] - Min[p] >= t[p]], {n, z}] (* A237834 *)
Table[Count[IntegerPartitions[n], _?(#[[1]]-#[[-1]]>=Length[#]&)], {n, 50}] (* Harvey P. Dale, Jul 21 2023 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Feb 16 2014
STATUS
approved