This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A344310 #13 Jun 06 2021 05:10:12 %S A344310 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 A344310 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 A344310 2,3,4,4,1,4,4,3,2,4,3,4,2,3,4,4,1,4,4 %N A344310 Number of knapsack partitions of n with largest part 4. %C A344310 An integer partition is knapsack if every distinct submultiset has a different sum. %C A344310 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 A344310 The initial values count the following partitions: %e A344310 4: (4) %e A344310 5: (4,1) %e A344310 6: (4,1,1) %e A344310 6: (4,2) %e A344310 7: (4,1,1,1) %e A344310 7: (4,2,1) %e A344310 7: (4,3) %e A344310 8: (4,4) %Y A344310 Cf. A108917, A275972, A326017, A326034, A343321. %K A344310 nonn %O A344310 0,7 %A A344310 _Fausto A. C. Cariboni_, May 14 2021