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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
Fausto A. C. Cariboni, Table of n, a(n) for n = 0..100
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
Sequence in context: A328221 A364913 A128215 * A097132 A321683 A321682
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 13 2019
EXTENSIONS
a(21)-a(22) from Jinyuan Wang, Jun 20 2020
a(23)-a(25) from Robert Price, Jun 19 2021
a(26)-a(46) from Fausto A. C. Cariboni, Feb 10 2022
STATUS
approved

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)