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A321142 Number of strict integer partitions of 2*n with no subset summing to n. 0
0, 1, 2, 3, 5, 7, 11, 15, 23, 30, 43, 57, 79, 102, 138, 174, 232, 292, 375, 471, 602, 741, 935, 1148, 1425, 1733, 2137, 2571, 3156, 3789, 4557, 5470, 6582, 7796, 9317, 11027, 13058, 15400, 18159, 21249, 24971, 29170, 33986, 39596, 46073, 53219, 61711, 71330, 82171 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..48.

EXAMPLE

The a(1) = 1 through a(8) = 23 partitions:

  (2)  (4)    (6)    (8)      (10)     (12)     (14)       (16)

       (3,1)  (4,2)  (5,3)    (6,4)    (7,5)    (8,6)      (9,7)

              (5,1)  (6,2)    (7,3)    (8,4)    (9,5)      (10,6)

                     (7,1)    (8,2)    (9,3)    (10,4)     (11,5)

                     (5,2,1)  (9,1)    (10,2)   (11,3)     (12,4)

                              (6,3,1)  (11,1)   (12,2)     (13,3)

                              (7,2,1)  (5,4,3)  (13,1)     (14,2)

                                       (7,3,2)  (6,5,3)    (15,1)

                                       (7,4,1)  (8,4,2)    (7,5,4)

                                       (8,3,1)  (8,5,1)    (7,6,3)

                                       (9,2,1)  (9,3,2)    (9,4,3)

                                                (9,4,1)    (9,5,2)

                                                (10,3,1)   (9,6,1)

                                                (11,2,1)   (10,4,2)

                                                (8,3,2,1)  (10,5,1)

                                                           (11,3,2)

                                                           (11,4,1)

                                                           (12,3,1)

                                                           (13,2,1)

                                                           (6,5,4,1)

                                                           (7,4,3,2)

                                                           (9,4,2,1)

                                                           (10,3,2,1)

MATHEMATICA

Table[Length[Select[IntegerPartitions[n], And[UnsameQ@@#, !Or@@Table[SameQ[Total[#[[s]]], n/2], {s, Subsets[Range[Length[#]]]}]]&]], {n, 2, 20, 2}]

CROSSREFS

Cf. A002219, A006827, A108917, A237258, A275972, A279791, A284640, A305551.

Sequence in context: A236102 A241726 A308990 * A024792 A280661 A055771

Adjacent sequences:  A321139 A321140 A321141 * A321143 A321144 A321145

KEYWORD

nonn

AUTHOR

Gus Wiseman, Oct 28 2018

EXTENSIONS

a(33)-a(48) from Giovanni Resta, Oct 30 2018

STATUS

approved

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Last modified May 28 21:37 EDT 2020. Contains 334690 sequences. (Running on oeis4.)