login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

Number of knapsack partitions of n with largest part 8.
3

%I #11 Jun 06 2021 02:52:49

%S 0,0,0,0,0,0,0,0,1,1,2,3,4,6,7,11,1,8,6,10,7,13,9,15,6,12,10,15,8,18,

%T 10,17,6,17,12,17,9,18,13,22,7,19,10,19,13,20,14,24,4,20,12,19,13,23,

%U 15,21,4,20,13,23,11,23,15,20,7,20,12,22,15,24,12,22

%N Number of knapsack partitions of n with largest part 8.

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

%C I computed terms a(n) for n = 0..40000 and the subsequence a(98)-a(937) of length 840 is repeated continuously.

%H Fausto A. C. Cariboni, <a href="/A342684/b342684.txt">Table of n, a(n) for n = 0..1000</a>

%e The initial nonzero values count the following partitions:

%e 8: (8)

%e 9: (8,1)

%e 10: (8,1,1), (8,2)

%e 11: (8,1,1,1), (8,2,1), (8,3)

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

%K nonn

%O 0,11

%A _Fausto A. C. Cariboni_, May 18 2021