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A325852 Number of (strict) integer partitions of n whose differences of all degrees are nonzero. 4
1, 1, 1, 2, 2, 3, 3, 5, 6, 6, 9, 11, 11, 15, 19, 19, 26, 31, 31, 41, 49, 53, 62, 75, 81, 97, 112, 124, 145, 171, 175, 215, 244, 274, 307, 344, 388, 446, 497, 561, 599, 700, 779, 881, 981, 1054, 1184, 1340, 1500, 1669, 1767, 2031, 2237, 2486, 2765, 2946, 3300 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

The differences of a sequence are defined as if the sequence were increasing, so for example the differences of (6,3,1) are (-3,-2). The zeroth differences are the sequence itself, while k-th differences for k > 0 are the differences of the (k-1)-th differences. The differences of all degrees of a sequence are the union of its zeroth through m-th differences, where m is the length of the sequence.

LINKS

Table of n, a(n) for n=0..56.

EXAMPLE

The a(1) = 1 through a(11) = 11 partitions (A = 10, B = 11):

  (1)  (2)  (3)   (4)   (5)   (6)   (7)    (8)    (9)    (A)    (B)

            (21)  (31)  (32)  (42)  (43)   (53)   (54)   (64)   (65)

                        (41)  (51)  (52)   (62)   (63)   (73)   (74)

                                    (61)   (71)   (72)   (82)   (83)

                                    (421)  (431)  (81)   (91)   (92)

                                           (521)  (621)  (532)  (A1)

                                                         (541)  (542)

                                                         (631)  (632)

                                                         (721)  (641)

                                                                (731)

                                                                (821)

MATHEMATICA

Table[Length[Select[IntegerPartitions[n], !MemberQ[Union@@Table[Differences[#, i], {i, Length[#]}], 0]&]], {n, 0, 30}]

CROSSREFS

The case for only degrees > 1 is A325874.

Cf. A049988, A175342, A238423, A279945, A295370, A325328, A325468, A325545, A325850, A325851, A325875.

Sequence in context: A325468 A320347 A178932 * A206439 A097450 A062303

Adjacent sequences:  A325849 A325850 A325851 * A325853 A325854 A325855

KEYWORD

nonn

AUTHOR

Gus Wiseman, May 31 2019

STATUS

approved

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Last modified February 17 12:32 EST 2020. Contains 331996 sequences. (Running on oeis4.)