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Number of knapsack partitions of n with largest part 10.
1

%I #8 Jun 06 2021 08:16:21

%S 0,0,0,0,0,0,0,0,0,0,1,1,2,3,4,6,7,11,12,17,1,13,9,16,11,20,14,24,16,

%T 25,9,27,14,29,19,32,16,34,19,37,11,32,17,38,19,32,22,41,19,40,14,38,

%U 22,41,22,39,18,44,26,46,8,46,24,38,23,40,21,48,28,42,12

%N Number of knapsack partitions of n with largest part 10.

%C An integer partition is knapsack if every distinct submultiset has a different sum.

%C I computed terms a(n) for n = 0..50000 and the subsequence a(162)-a(2681) of length 2520 is repeated continuously.

%H Fausto A. C. Cariboni, <a href="/A344635/b344635.txt">Table of n, a(n) for n = 0..3000</a>

%e The initial nonzero values count the following partitions:

%e 10: (10)

%e 11: (10,1)

%e 12: (10,1,1), (10,2)

%e 13: (10,1,1,1), (10,2,1), (10,3)

%Y Cf. A108917, A275972, A326017, A326034, A342684, A343321, A344310, A344340, A344412, A344625.

%K nonn

%O 0,13

%A _Fausto A. C. Cariboni_, May 25 2021