cp's OEIS Frontend

A325676 Number of compositions of n such that every distinct consecutive subsequence has a different sum.

%I A325676 #23 Feb 12 2022 10:42:28
%S A325676 1,1,2,4,5,10,12,24,26,47,50,96,104,172,188,322,335,552,590,938,1002,
%T A325676 1612,1648,2586,2862,4131,4418,6718,7122,10332,11166,15930,17446,
%U A325676 24834,26166,37146,41087,55732,59592,84068,89740,122106,133070,177876,194024,262840,278626
%N A325676 Number of compositions of n such that every distinct consecutive subsequence has a different sum.
%C A325676 A composition of n is a finite sequence of positive integers summing to n.
%C A325676 Compare to the definition of knapsack partitions (A108917).
%H A325676 Fausto A. C. Cariboni, <a href="/A325676/b325676.txt">Table of n, a(n) for n = 0..100</a>
%e A325676 The distinct consecutive subsequences of (1,4,4,3) together with their sums are:
%e A325676    1: {1}
%e A325676    3: {3}
%e A325676    4: {4}
%e A325676    5: {1,4}
%e A325676    7: {4,3}
%e A325676    8: {4,4}
%e A325676    9: {1,4,4}
%e A325676   11: {4,4,3}
%e A325676   12: {1,4,4,3}
%e A325676 Because the sums are all different, (1,4,4,3) is counted under a(12).
%e A325676 The a(1) = 1 through a(6) = 12 compositions:
%e A325676   (1)  (2)   (3)    (4)     (5)      (6)
%e A325676        (11)  (12)   (13)    (14)     (15)
%e A325676              (21)   (22)    (23)     (24)
%e A325676              (111)  (31)    (32)     (33)
%e A325676                     (1111)  (41)     (42)
%e A325676                             (113)    (51)
%e A325676                             (122)    (114)
%e A325676                             (221)    (132)
%e A325676                             (311)    (222)
%e A325676                             (11111)  (231)
%e A325676                                      (411)
%e A325676                                      (111111)
%t A325676 Table[Length[Select[Join@@Permutations/@IntegerPartitions[n],UnsameQ@@Total/@Union[ReplaceList[#,{___,s__,___}:>{s}]]&]],{n,0,15}]
%Y A325676 Cf. A000079, A103295, A108917, A169942, A235998, A321143.
%Y A325676 Cf. A325466, A325545, A325680, A325682, A325685, A325687, A325688.
%K A325676 nonn
%O A325676 0,3
%A A325676 _Gus Wiseman_, May 13 2019
%E A325676 a(21)-a(22) from _Jinyuan Wang_, Jun 20 2020
%E A325676 a(23)-a(25) from _Robert Price_, Jun 19 2021
%E A325676 a(26)-a(46) from _Fausto A. C. Cariboni_, Feb 10 2022