OFFSET
1,7
FORMULA
From Omar E. Pol, Sep 11 2021: (Start)
EXAMPLE
a(8) = 3 counts these partitions: 7+1, 6+2, 5+2+1.
MATHEMATICA
z = 70; q[n_] := q[n] = Select[IntegerPartitions[n], Max[Length /@ Split@#] == 1 &]; p1[p_] := p1[p] = DeleteDuplicates[p]; t[p_] := t[p] = Length[p1[p]];
Table[Count[q[n], p_ /; Max[p] - Min[p] < t[p]], {n, z}] (* A001227 *)
Table[Count[q[n], p_ /; Max[p] - Min[p] <= t[p]], {n, z}] (* A003056 *)
Table[Count[q[n], p_ /; Max[p] - Min[p] == t[p]], {n, z}] (* A238005 *)
Table[Count[q[n], p_ /; Max[p] - Min[p] > t[p]], {n, z}] (* A238006 *)
Table[Count[q[n], p_ /; Max[p] - Min[p] >= t[p]], {n, z}] (* A238007 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Feb 17 2014
STATUS
approved