The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A237834 Number of partitions of n such that (greatest part) - (least part) >= number of parts. 5
 0, 0, 0, 1, 1, 3, 4, 7, 10, 15, 20, 30, 39, 54, 71, 96, 123, 163, 208, 270, 342, 437, 548, 695, 865, 1083, 1341, 1666, 2048, 2527, 3089, 3784, 4604, 5606, 6786, 8222, 9907, 11940, 14331, 17196, 20554, 24563, 29252, 34820, 41327, 49016, 57982, 68545, 80833 (list; graph; refs; listen; history; text; internal format)
 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 A237830(n)+a(n) = A000041(n). - R. J. Mathar, Nov 24 2017 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 *) CROSSREFS Cf. A237830, A237831, A237832, A237833. Sequence in context: A050572 A249668 A105343 * A147955 A147789 A047625 Adjacent sequences:  A237831 A237832 A237833 * A237835 A237836 A237837 KEYWORD nonn,easy AUTHOR Clark Kimberling, Feb 16 2014 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 2 10:24 EST 2021. Contains 349437 sequences. (Running on oeis4.)