A340732 Number of partitions of n into 4 parts such that the product of the smallest and largest parts is equal to the product of the middle two parts.

0, 0, 0, 0, 1, 0, 1, 0, 2, 1, 2, 0, 4, 0, 3, 2, 5, 0, 6, 0, 7, 3, 5, 0, 10, 3, 6, 4, 10, 0, 13, 0, 11, 5, 8, 6, 18, 0, 9, 6, 18, 0, 19, 0, 16, 13, 11, 0, 25, 6, 19, 8, 19, 0, 24, 10, 26, 9, 14, 0, 38, 0, 15, 19, 26, 12, 31, 0, 25, 11, 35, 0, 45, 0, 18, 23, 28, 15, 37, 0, 45, 19

Offset

0,9

Links

Table of n, a(n) for n=0..81.

Index entries for sequences related to partitions

Formula

a(n) = Sum_{k=1..floor(n/4)} Sum_{j=k..floor((n-k)/3)} Sum_{i=j..floor((n-j-k)/2)} [j*i = k*(n-i-j-k)], where [ ] is the Iverson bracket.

Mathematica

Table[Sum[Sum[Sum[KroneckerDelta[j*i, k*(n - i - j - k)], {i, j, Floor[(n - j - k)/2]}], {j, k, Floor[(n - k)/3]}], {k, Floor[n/4]}], {n, 0, 100}]

Prog

(PARI) for(n=0, 70, my(count=0); forpart(p=n, if(#p==4, count+=(p[1]*p[4]==p[2]*p[3]))); print1(count, ", ")) \\ Hugo Pfoertner, Jan 18 2021

Crossrefs

Sequence in context: A374354 A373043 A240205 * A050319 A132456 A257873

Adjacent sequences: A340729 A340730 A340731 * A340733 A340734 A340735

Keyword

nonn

Author

Wesley Ivan Hurt, Jan 17 2021

Status

approved