A351740 Total number of parts in all partitions of n into parts of size 1, 5, 10 or 25.

0, 1, 2, 3, 4, 6, 8, 10, 12, 14, 19, 23, 27, 31, 35, 44, 50, 56, 62, 68, 83, 92, 101, 110, 119, 141, 154, 167, 180, 193, 226, 244, 262, 280, 298, 343, 367, 391, 415, 439, 500, 531, 562, 593, 624, 702, 741, 780, 819, 858, 959, 1008, 1057, 1106, 1155, 1280, 1340

Offset: 0

Author

Alois P. Heinz, Feb 17 2022

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A001299, A351725.

Programs

Maple

b:= proc(n, i) option remember; `if`(n=0 or i=1, [1, n], b(n, i-1)+
     (p->`if`(p>n, 0, (t->t+[0, t[1]])(b(n-p, i))))([1, 5, 10, 25][i]))
    end:
a:= n-> b(n, 4)[2]:
seq(a(n), n=0..100);

Formula

a(n) = Sum_{k=0..n} k * A351725(n,k).