A350534 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.

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, 52, 0, 36, 20, 16, 24, 88, 0, 18, 24, 74, 0, 76, 0, 51, 60, 22, 0, 121, 36, 60, 32, 61, 0, 100, 40, 108, 36, 28, 0, 198, 0, 30, 88, 125, 48, 124, 0, 81, 44, 140, 0, 243, 0, 36, 104

Offset

0,6

Links

David A. Corneth, Table of n, a(n) for n = 0..10000

Index entries for sequences related to partitions

Formula

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.

Example

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.

Mathematica

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}]

Prog

(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

Crossrefs

Cf. A072670, A183003, A350497.

Sequence in context: A274441 A213859 A330492 * A101336 A300001 A137218

Adjacent sequences: A350531 A350532 A350533 * A350535 A350536 A350537

Keyword

nonn

Author

Wesley Ivan Hurt, Jan 04 2022

Status

approved