This site is supported by donations to The OEIS Foundation.

 Annual Appeal: Please make a donation to keep the OEIS running. In 2018 we replaced the server with a faster one, added 20000 new sequences, and reached 7000 citations (often saying "discovered thanks to the OEIS"). Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A240059 Number of partitions of n such that m(1) > m(3), where m = multiplicity. 2
 0, 1, 1, 2, 2, 5, 6, 10, 12, 20, 25, 37, 46, 67, 84, 116, 145, 197, 246, 325, 404, 527, 653, 837, 1032, 1310, 1609, 2018, 2467, 3070, 3738, 4612, 5591, 6854, 8277, 10080, 12125, 14688, 17604, 21212, 25333, 30389, 36172, 43201, 51256, 60981, 72132, 85498 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS FORMULA a(n) + A182714(n) + A240058(n) = A000041(n) for n >= 0. EXAMPLE a(6) counts these 6 partitions:  51, 411, 3111, 2211, 21111, 111111. MATHEMATICA z = 60; f[n_] := f[n] = IntegerPartitions[n]; t1 = Table[Count[f[n], p_ /; Count[p, 1] < Count[p, 3]], {n, 0, z}]  (* A182714 *) t2 = Table[Count[f[n], p_ /; Count[p, 1] <= Count[p, 3]], {n, 0, z}] (* A182714(n+3) *) t3 = Table[Count[f[n], p_ /; Count[p, 1] == Count[p, 3]], {n, 0, z}] (* A240058 *) t4 = Table[Count[f[n], p_ /; Count[p, 1] > Count[p, 3]], {n, 0, z}]  (* A240059 *) t5 = Table[Count[f[n], p_ /; Count[p, 1] >= Count[p, 3]], {n, 0, z}] (* A240059(n+1) *) CROSSREFS Cf. A182714, A240058, A000041. Sequence in context: A098507 A097066 A035548 * A288766 A007988 A241449 Adjacent sequences:  A240056 A240057 A240058 * A240060 A240061 A240062 KEYWORD nonn,easy AUTHOR Clark Kimberling, Mar 31 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 15 19:06 EST 2018. Contains 318151 sequences. (Running on oeis4.)