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A325676 Number of compositions of n such that every distinct consecutive subsequence has a different sum. 34
1, 1, 2, 4, 5, 10, 12, 24, 26, 47, 50, 96, 104, 172, 188, 322, 335, 552, 590, 938, 1002 (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

Table of n, a(n) for n=0..20.

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

Cf. A000079, A103295, A108917, A169942, A235998, A321143.

Cf. A325466, A325545, A325680, A325682, A325685, A325687, A325688.

Sequence in context: A133732 A328221 A128215 * A097132 A321683 A321682

Adjacent sequences:  A325673 A325674 A325675 * A325677 A325678 A325679

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, May 13 2019

STATUS

approved

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Last modified June 4 03:40 EDT 2020. Contains 334815 sequences. (Running on oeis4.)