A025437 Number of partitions of n into 4 distinct squares.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 2, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 2, 0, 0, 1, 2, 1, 0, 1, 2, 0, 1, 1, 0, 1, 0, 1, 3, 1, 0, 2, 2, 0, 0, 2, 2, 1, 0, 0, 3, 2, 0, 2, 4, 1, 0, 2, 0, 1, 2, 1, 3, 1, 0, 2, 4, 2, 0, 2, 4, 2, 0, 0, 3, 2, 0, 3, 3, 0, 1, 4, 2, 2

Offset

0,31

Comments

Zero counts as a distinct square. - Harvey P. Dale, Aug 28 2025

Links

Table of n, a(n) for n=0..107.

Mathematica

c[k_]:=Table[Count[IntegerPartitions[n, {k}], _?(AllTrue[Sqrt[#], IntegerQ]&&DuplicateFreeQ[#]&)], {n, 0, 110}]; c[3]+c[4] (* Harvey P. Dale, Aug 28 2025 *)

Crossrefs

Sequence in context: A391437 A127475 A086014 * A066032 A035187 A291147

Adjacent sequences: A025434 A025435 A025436 * A025438 A025439 A025440

Keyword

nonn

Author

David W. Wilson

Status

approved