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

0,3

Links

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

Formula

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

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);

Crossrefs

Cf. A001299, A351725.

Sequence in context: A078769 A064375 A037229 * A230374 A007183 A067783

Adjacent sequences: A351737 A351738 A351739 * A351741 A351742 A351743

Keyword

nonn

Author

Alois P. Heinz, Feb 17 2022

Status

approved