

A308410


a(n) is the number of partitions p = p(1) >= p(2) >= ... >= p(k) of n whose alternating sum is a part of p.


0



1, 1, 3, 2, 5, 6, 10, 10, 20, 18, 33, 35, 55, 59, 92, 97, 146, 161, 231, 251, 363, 393, 551, 609, 828, 924, 1240, 1382, 1824, 2055, 2665, 3004, 3870, 4359, 5551, 6280, 7910, 8957, 11201, 12683, 15728, 17857, 21951, 24939, 30472, 34625, 42031, 47803, 57677
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OFFSET

1,3


LINKS

Table of n, a(n) for n=1..49.


EXAMPLE

The a(6) = 6 partitions of 6 to be counted are these:
[6] has alternating sum 6, which is a part,
[4,2] has alternating sum 4  2 = 2, a part,
[4,1,1] has alternating sum 4  1 + 1 = 4,
[3,2,1] has alternating sum 3  2 + 1 = 2,
[2,2,2] has alternating sum 2  2 + 1 = 2, and
[2,1,1,1,1] has alternating sum 2  1 + 1  1 + 1  1 = 2.


MATHEMATICA

Map[Count[Map[Apply[MemberQ, {#, Total[Map[
Total, {Take[##], Drop[##]} &[#, {1, 1, 2}] {1, 1}]]}] &,
IntegerPartitions[#]], True] &, Range[40]]
(* Peter J. C. Moses, May 25 2019 *)


CROSSREFS

Cf. A000041, A308230.
Sequence in context: A194012 A255556 A331462 * A286111 A240574 A050061
Adjacent sequences: A308407 A308408 A308409 * A308411 A308412 A308413


KEYWORD

nonn,easy


AUTHOR

Clark Kimberling, Jun 05 2019


STATUS

approved



