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
Fausto A. C. Cariboni, Table of n, a(n) for n = 0..250
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
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 31 2019
STATUS
approved