A344310 - OEIS

%I #13 Jun 06 2021 05:10:12

%S 0,0,0,0,1,1,2,3,1,2,3,3,1,3,3,3,2,3,3,4,2,3,4,4,1,4,4,3,2,4,3,4,2,3,

%T 4,4,1,4,4,3,2,4,3,4,2,3,4,4,1,4,4,3,2,4,3,4,2,3,4,4,1,4,4,3,2,4,3,4,

%U 2,3,4,4,1,4,4,3,2,4,3,4,2,3,4,4,1,4,4

%N Number of knapsack partitions of n with largest part 4.

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

%C I computed terms a(n) for n = 0..10000 and (3, 4, 2, 3, 4, 4, 1, 4, 4, 3, 2, 4) is repeated continuously starting at a(18).

%e The initial values count the following partitions:

%e    4: (4)

%e    5: (4,1)

%e    6: (4,1,1)

%e    6: (4,2)

%e    7: (4,1,1,1)

%e    7: (4,2,1)

%e    7: (4,3)

%e    8: (4,4)

%Y Cf. A108917, A275972, A326017, A326034, A343321.

%K nonn

%O 0,7

%A _Fausto A. C. Cariboni_, May 14 2021