|
|
A325676
|
|
Number of compositions of n such that every distinct consecutive subsequence has a different sum.
|
|
57
|
|
|
1, 1, 2, 4, 5, 10, 12, 24, 26, 47, 50, 96, 104, 172, 188, 322, 335, 552, 590, 938, 1002, 1612, 1648, 2586, 2862, 4131, 4418, 6718, 7122, 10332, 11166, 15930, 17446, 24834, 26166, 37146, 41087, 55732, 59592, 84068, 89740, 122106, 133070, 177876, 194024, 262840, 278626
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
COMMENTS
|
A composition of n is a finite sequence of positive integers summing to n.
Compare to the definition of knapsack partitions (A108917).
|
|
LINKS
|
|
|
EXAMPLE
|
The distinct consecutive subsequences of (1,4,4,3) together with their sums are:
1: {1}
3: {3}
4: {4}
5: {1,4}
7: {4,3}
8: {4,4}
9: {1,4,4}
11: {4,4,3}
12: {1,4,4,3}
Because the sums are all different, (1,4,4,3) is counted under a(12).
The a(1) = 1 through a(6) = 12 compositions:
(1) (2) (3) (4) (5) (6)
(11) (12) (13) (14) (15)
(21) (22) (23) (24)
(111) (31) (32) (33)
(1111) (41) (42)
(113) (51)
(122) (114)
(221) (132)
(311) (222)
(11111) (231)
(411)
(111111)
|
|
MATHEMATICA
|
Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], UnsameQ@@Total/@Union[ReplaceList[#, {___, s__, ___}:>{s}]]&]], {n, 0, 15}]
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|