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A320347
Number of partitions of n into distinct parts (a_1, a_2, ... , a_m) (a_1 > a_2 > ... > a_m and Sum_{k=1..m} a_k = n) such that a1 - a2, a2 - a3, ..., a_{m-1} - a_m are different.
19
1, 1, 2, 2, 3, 3, 5, 6, 6, 9, 11, 10, 15, 18, 19, 24, 31, 29, 40, 44, 51, 56, 72, 69, 90, 97, 114, 125, 154, 151, 192, 207, 237, 255, 304, 314, 377, 401, 457, 493, 573, 596, 698, 750, 845, 905, 1034, 1104, 1255, 1354, 1507, 1624, 1817, 1955, 2178, 2357, 2605, 2794, 3077, 3380
OFFSET
1,3
COMMENTS
In other words, a(n) is the number of strict integer partitions of n with distinct first differences. - Gus Wiseman, Mar 25 2021
EXAMPLE
n = 9
[9] ooooooooo
------------------------------------
[8, 1] *******o a_1 - a_2 = 7.
oooooooo
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[7, 2] *****oo a_1 - a_2 = 5.
ooooooo
------------------------------------
[6, 3] ***ooo a_1 - a_2 = 3.
oooooo
------------------------------------
[6, 2, 1] *o a_2 - a_3 = 1.
****oo a_1 - a_2 = 4.
oooooo
------------------------------------
[5, 4] *oooo a_1 - a_2 = 1.
ooooo
------------------------------------
a(9) = 6.
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&UnsameQ@@Differences[#]&]], {n, 0, 30}] (* Gus Wiseman, Mar 27 2021 *)
CROSSREFS
The equal instead of distinct version is A049980.
The non-strict version is A325325 (ranking: A325368).
The non-strict ordered version is A325545.
The version for first quotients is A342520 (non-strict: A342514).
Sequence in context: A316313 A325876 A325468 * A178932 A325852 A332668
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Oct 11 2018
STATUS
approved