A160644 First of two sequences bisecting the second differences of the partition numbers (see A053445).

1, 1, 2, 3, 4, 7, 10, 14, 22, 32, 45, 67, 95, 134, 192, 269, 373, 521, 718, 983, 1346, 1827, 2465, 3323, 4449, 5929, 7882, 10426, 13735, 18047, 23613, 30788, 40034, 51877, 67013, 86341, 110905, 142063, 181529, 231340, 294077, 372977, 471908, 595725, 750432

Offset

1,3

Comments

A160644 also counts selected unrestricted partition having an EVEN total and with minimum part two. For example it counts these three partitions of eight: 4+4, 3+3+2, and 2+2+2+2.

Links

Nathaniel Johnston, Table of n, a(n) for n = 1..2500

Example

A053445 begins
1 0 1 0 2 0 3 1 4 2 7 3 10 7 14 11 22 17 32 28 45 ...
therefore a(n) begins
1 1 2 3 4 7 10 14 22 32 45 67 95 134 192 ...

Mathematica

Take[Differences[PartitionsP[Range[0, 100]], 2], {1, -1, 2}] (* Harvey P. Dale, Aug 05 2019 *)

Crossrefs

Cf. A000041, A002685, A053445, A160643, A161921 (the other bisection).

Sequence in context: A240489 A056513 A056518 * A347734 A267459 A330357

Adjacent sequences: A160641 A160642 A160643 * A160645 A160646 A160647

Keyword

easy,nonn

Author

Alford Arnold, May 21 2009

Status

approved