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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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,13
LINKS
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
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Jan 06 2021
STATUS
approved

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Last modified May 22 10:24 EDT 2024. Contains 372745 sequences. (Running on oeis4.)