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 A237832 Number of partitions of n such that (greatest part) - (least part) = number of parts. 12

%I

%S 0,0,0,1,0,2,1,3,3,5,4,10,8,13,15,22,22,34,36,51,58,75,85,116,130,165,

%T 194,244,281,355,409,505,591,718,839,1022,1186,1425,1668,1994,2319,

%U 2765,3213,3805,4429,5214,6052,7119,8243,9645,11169,13026,15046,17511

%N Number of partitions of n such that (greatest part) - (least part) = number of parts.

%H R. J. Mathar, <a href="/A237832/b237832.txt">Table of n, a(n) for n = 1..96</a>

%H George E. Andrews, <a href="http://www.personal.psu.edu/gea1/pdf/315.pdf">4-Shadows in q-Series and the Kimberling Index</a>, Preprint, May 15, 2016.

%F A237830(n) + a(n) + A237833(n) = A000041(n). - _R. J. Mathar_, Nov 24 2017

%e a(6) = 2 counts these partitions: 4+2, 4+1+1.

%t z = 60; q[n_] := q[n] = IntegerPartitions[n]; t[p_] := t[p] = Length[p];

%t Table[Count[q[n], p_ /; Max[p] - Min[p] < t[p]], {n, z}] (* A237830 *)

%t Table[Count[q[n], p_ /; Max[p] - Min[p] <= t[p]], {n, z}] (* A237831 *)

%t Table[Count[q[n], p_ /; Max[p] - Min[p] == t[p]], {n, z}] (* A237832 *)

%t Table[Count[q[n], p_ /; Max[p] - Min[p] > t[p]], {n, z}] (* A237833 *)

%t Table[Count[q[n], p_ /; Max[p] - Min[p] >= t[p]], {n, z}] (* A237834 *)

%Y Cf. A237830, A237831, A237833, A237834.

%K nonn,easy

%O 1,6

%A _Clark Kimberling_, Feb 16 2014

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Last modified November 25 20:20 EST 2020. Contains 338627 sequences. (Running on oeis4.)