

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, 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
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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((nk)/3)} Sum_{i=j..floor((njk)/2)} [j*i = k*(nijk)], 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: A276669 A307596 A240205 * A050319 A132456 A257873
Adjacent sequences: A340729 A340730 A340731 * A340733 A340734 A340735


KEYWORD

nonn


AUTHOR

Wesley Ivan Hurt, Jan 17 2021


STATUS

approved



