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, 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

Offset

0,13

Links

Table of n, a(n) for n=0..82.

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)} [k*(k+1) = n-i-j], 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

Sequence in context: A219238 A025918 A030425 * A076879 A225230 A367106

Adjacent sequences: A340388 A340389 A340390 * A340392 A340393 A340394

Keyword

nonn

Author

Wesley Ivan Hurt, Jan 06 2021

Status

approved