|
%I #7 Apr 19 2014 19:12:42
%S 0,0,0,0,0,1,2,4,6,12,17,26,38,54,76,107,142,192,259,337,443,577,743,
%T 948,1213,1532,1935,2427,3031,3765,4681,5762,7097,8704,10644,12966,
%U 15775,19104,23115,27874,33546,40257,48259,57656,68809,81929,97378,115495
%N Number of partitions p of n such that (number of distinct parts of p) < max(p) - min(p).
%F a(n) + A239958(n) = A000041(n) for n >= 0.
%e a(7) counts these 4 partitions: 61, 52, 511, 1111111.
%t z = 60; d[p_] := d[p] = Length[DeleteDuplicates[p]]; f[p_] := f[p] = Max[p] - Min[p]; g[n_] := g[n] = IntegerPartitions[n];
%t Table[Count[g[n], p_ /; d[p] < f[p]], {n, 0, z}] (*A239954*)
%t Table[Count[g[n], p_ /; d[p] <= f[p]], {n, 0, z}] (*A239955*)
%t Table[Count[g[n], p_ /; d[p] == f[p]], {n, 0, z}] (*A239956*)
%t Table[Count[g[n], p_ /; d[p] > f[p]], {n, 0, z}] (*A034296*)
%t Table[Count[g[n], p_ /; d[p] >= f[p]], {n, 0, z}] (*A239958*)
%Y Cf. A239955, A239956, A034296, A239958.
%K nonn,easy
%O 0,7
%A _Clark Kimberling_, Mar 30 2014
|
