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

%I A351740 #7 Feb 17 2022 11:39:52
%S A351740 0,1,2,3,4,6,8,10,12,14,19,23,27,31,35,44,50,56,62,68,83,92,101,110,
%T A351740 119,141,154,167,180,193,226,244,262,280,298,343,367,391,415,439,500,
%U A351740 531,562,593,624,702,741,780,819,858,959,1008,1057,1106,1155,1280,1340
%N A351740 Total number of parts in all partitions of n into parts of size 1, 5, 10 or 25.
%H A351740 Alois P. Heinz, <a href="/A351740/b351740.txt">Table of n, a(n) for n = 0..10000</a>
%F A351740 a(n) = Sum_{k=0..n} k * A351725(n,k).
%p A351740 b:= proc(n, i) option remember; `if`(n=0 or i=1, [1, n], b(n, i-1)+
%p A351740      (p->`if`(p>n, 0, (t->t+[0, t[1]])(b(n-p, i))))([1, 5, 10, 25][i]))
%p A351740     end:
%p A351740 a:= n-> b(n, 4)[2]:
%p A351740 seq(a(n), n=0..100);
%Y A351740 Cf. A001299, A351725.
%K A351740 nonn
%O A351740 0,3
%A A351740 _Alois P. Heinz_, Feb 17 2022