A303052 Total area of all squares with squarefree side length |s - t|, such that n = s + t, and s < t, where s and t are positive integers.

0, 0, 1, 4, 10, 4, 35, 40, 84, 40, 84, 140, 205, 140, 374, 336, 599, 336, 888, 336, 1249, 336, 1690, 820, 2219, 820, 2219, 1496, 2219, 1496, 3060, 2396, 4021, 2396, 5110, 3552, 6335, 3552, 7704, 4996, 9225, 4996, 10906, 6760, 12755, 6760, 12755, 8876, 14964

Offset

1,4

Links

Table of n, a(n) for n=1..49.

Index entries for sequences related to partitions

Formula

a(n) = Sum_{i=1..floor((n-1)/2)} (n-2*i)^2 * mu(n-2*i)^2, where mu is the Möbius function (A008683).

Mathematica

Table[Sum[(n - 2 i)^2 MoebiusMu[n - 2 i]^2, {i, Floor[(n - 1)/2]}], {n, 100}]

Prog

(PARI) a(n) = sum(i=1, (n-1)\2, (n-2*i)^2*moebius(n-2*i)^2); \\ Michel Marcus, Apr 17 2018

Crossrefs

Cf. A008683.

Sequence in context: A128505 A336988 A200454 * A003564 A347116 A205016

Adjacent sequences: A303049 A303050 A303051 * A303053 A303054 A303055

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Apr 17 2018

Status

approved