This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A072380 Third differences of partition numbers A000041. 10
 -1, 1, -1, 2, -2, 3, -2, 3, -2, 5, -4, 7, -3, 7, -3, 11, -5, 15, -4, 17, -2, 24, -4, 32, 1, 38, 5, 53, 7, 70, 18, 86, 33, 115, 45, 152, 74, 191, 109, 254, 150, 331, 218, 420, 307, 551, 410, 716, 567, 913, 767, 1186, 1015, 1529, 1358, 1951, 1799, 2513, 2344, 3222, 3079, 4096, 4009, 5237, 5173 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Comtet appears to say this is nonnegative, which is only true for n sufficiently large. An explanation is given by Odlyzko. - Moshe Shmuel Newman, Jun 11 2006 REFERENCES L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 115. A. M. Odlyzko, Differences of the partition function, Acta Arith., 49 (1988), pp. 237-254 LINKS Vaclav Kotesovec, Table of n, a(n) for n = 0..10000 Almkvist, Gert, "On the differences of the partition function", Acta Arith., 61.2 (1992), 173-181. FORMULA a(n) ~ exp(Pi*sqrt(2*n/3)) * Pi^3 / (72 * sqrt(2) * n^(5/2)). - Vaclav Kotesovec, Oct 06 2017 MATHEMATICA Differences[PartitionsP[Range[0, 70]], 3] (* Harvey P. Dale, Aug 16 2012 *) CROSSREFS Cf. A000041, A002865, A053445, A081094, A081095. Sequence in context: A105560 A165916 A096013 * A144910 A080330 A152872 Adjacent sequences:  A072377 A072378 A072379 * A072381 A072382 A072383 KEYWORD sign AUTHOR N. J. A. Sloane, Apr 25 2003 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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified October 23 01:57 EDT 2018. Contains 316518 sequences. (Running on oeis4.)