This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A236544 Number of partitions of n for which (number of occurrences of the least part) > (number of occurrences of greatest part). 3
 0, 0, 0, 1, 2, 3, 7, 9, 15, 21, 32, 41, 62, 80, 109, 144, 196, 246, 331, 418, 542, 688, 882, 1097, 1397, 1739, 2176, 2690, 3352, 4108, 5082, 6206, 7603, 9255, 11277, 13632, 16540, 19931, 24023, 28826, 34618, 41361, 49461, 58900, 70117, 83238, 98766, 116804 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS The partitions of n are partitioned by the partitions counted by A236543, A236544, A236545 (see Example); consequently, A000041(n) = A236543(n) + A236544(n) + A236545(n) for n >= 1. LINKS EXAMPLE Among the 15 partitions of 7, the following 6 have #(occurrences of  least part) = #(occurrences of greatest part): 7, 61, 52, 43, 421, 111111; the following 7 have " > " in place of " = ": 511, 4111, 322, 3211, 31111, 22111, 211111; and the remaining 2, have " < ": 331, 221. MATHEMATICA z = 65; s = Map[Map[Length, {Select[#, First[#] == Last[#] &], Select[#, First[#] > Last[#] &], Select[#, First[#] < Last[#] &]} &[Map[{Count[#, Min[#]], Count[#, Max[#]]} &, IntegerPartitions[#]]]] &, Range[z]]; t = Flatten[s]; t1 = Table[t[[3 k - 2]], {k, 1, z}] (* A236543 *) t2 = Table[t[[3 k - 1]], {k, 1, z}] (* A236544 *) t3 = Table[t[[3 k]], {k, 1, z}]     (* A236545 *) (* Peter J. C. Moses, Jan 28 2014 *) CROSSREFS Cf. A236543, A236545, A000041. Sequence in context: A294122 A211539 A109660 * A075855 A140189 A327066 Adjacent sequences:  A236541 A236542 A236543 * A236545 A236546 A236547 KEYWORD nonn,easy AUTHOR Clark Kimberling, Jan 28 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 10 15:09 EST 2019. Contains 329896 sequences. (Running on oeis4.)