

A340391


Number of partitions of n into 4 parts such that the largest part is equal to the square of the smallest part.


0



0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 2, 1, 1, 0, 0, 0, 1, 1, 2, 2, 3, 3, 4, 3, 3, 2, 3, 2, 3, 2, 3, 3, 4, 4, 5, 5, 6, 6, 8, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 7, 9, 9, 11, 11, 13, 13, 15, 14, 15, 14, 15, 14, 15, 14, 15, 14, 16, 15, 17, 16, 18, 17, 19, 18, 20, 19, 21, 20, 22
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OFFSET

0,13


LINKS



FORMULA

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


MATHEMATICA

Table[Sum[Sum[Sum[KroneckerDelta[k*(k + 1), n  i  j], {i, j, Floor[(n  j  k)/2]}], {j, k, Floor[(n  k)/3]}], {k, Floor[n/4]}], {n, 0, 100}]
Table[Count[IntegerPartitions[n, {4}], _?(#[[1]]==#[[1]]^2&)], {n, 0, 90}] (* Harvey P. Dale, May 22 2021 *)


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



