A350534 - OEIS

%I #15 Jan 11 2022 11:28:22

%S 0,0,0,1,0,2,0,3,4,4,0,11,0,6,8,16,0,18,0,21,12,10,0,40,16,12,16,31,0,

%T 52,0,36,20,16,24,88,0,18,24,74,0,76,0,51,60,22,0,121,36,60,32,61,0,

%U 100,40,108,36,28,0,198,0,30,88,125,48,124,0,81,44,140,0,243,0,36,104

%N Sum of the largest parts of the partitions of n into 3 parts whose largest part is equal to the product of the other two.

%H David A. Corneth, <a href="/A350534/b350534.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>

%F a(n) = Sum_{k=1..floor(n/3)} Sum_{i=k..floor((n-k)/2)} [n-i-k = i*k] * (n-i-k), where [ ] is the Iverson bracket.

%e a(13) = 6 since we have 13 = 1+6+6, whose largest part is 6. Partitions not counted: 1+1+11, 1+2+10, 1+3+9, 1+4+8, 1+5+7, 2+2+9, 2+3+8, 2+4+7, 2+5+6, 3+3+7, 3+4+6, 3+5+5, 4+4+5.

%t Table[Sum[Sum[(n - i - k) KroneckerDelta[(n - i - k), (i*k)], {i, k, Floor[(n - k)/2]}], {k, Floor[n/3]}], {n, 0, 100}]

%o (PARI) first(n) = {my(res = vector(n)); for(i = 1, n \ 2, for(j = i, n\i, c = i + j + i*j; if(c <= n, res[c] += i*j))); concat(0, res)} \\ _David A. Corneth_, Jan 07 2022

%Y Cf. A072670, A183003, A350497.

%K nonn

%O 0,6

%A _Wesley Ivan Hurt_, Jan 04 2022