A307608 Number of partitions of n^2 into consecutive positive squares.

1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1

Offset

1,5

Links

Table of n, a(n) for n=1..93.

Index entries for sequences related to sums of squares

Formula

a(n) = [x^(n^2)] Sum_{i>=1} Sum_{j>=i} Product_{k=i..j} x^(k^2).

a(n) = A296338(A000290(n)).

a(n) >= 2 for n in A097812.

Example

29^2 = 20^2 + 21^2, so a(29) = 2.

Crossrefs

Cf. A000290, A030273, A034705, A037444, A097812, A151557, A296338.

Sequence in context: A298481 A324872 A375873 * A323022 A284562 A349542

Adjacent sequences: A307605 A307606 A307607 * A307609 A307610 A307611

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 18 2019

Status

approved