The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

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