

A340755


Number of partitions of n into 4 parts such that the sum of the smallest two parts and the sum of the largest two parts are both squarefree.


0



0, 0, 0, 0, 1, 1, 0, 2, 4, 5, 2, 1, 7, 10, 4, 11, 23, 22, 16, 26, 35, 31, 28, 28, 52, 48, 43, 49, 80, 73, 34, 58, 105, 107, 70, 99, 195, 157, 89, 159, 258, 227, 164, 238, 374, 327, 251, 282, 480, 404, 306, 306, 539, 481, 402, 290, 566, 528, 472, 352, 630, 582, 495, 500, 766, 648, 598, 546, 1033, 733, 772, 616, 1428, 873, 952, 938, 1515, 1111, 1028, 1239, 1742
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OFFSET

0,8


LINKS

Table of n, a(n) for n=0..80.
Index entries for sequences related to partitions


FORMULA

a(n) = Sum_{k=1..floor(n/4)} Sum_{j=k..floor((nk)/3)} Sum_{i=j..floor((njk)/3)} mu(k+j)^2 * mu(njk)^2, where mu is the Möbius function (A008683).


MATHEMATICA

Table[Sum[Sum[Sum[MoebiusMu[k + j]^2*MoebiusMu[n  j  k]^2, {i, j, Floor[(n  j  k)/2]}], {j, k, Floor[(n  k)/3]}], {k, Floor[n/4]}], {n, 0, 80}]


CROSSREFS

Cf. A008683 (mu).
Sequence in context: A075884 A030750 A286147 * A059215 A125142 A234350
Adjacent sequences: A340752 A340753 A340754 * A340756 A340757 A340758


KEYWORD

nonn


AUTHOR

Wesley Ivan Hurt, Jan 19 2021


STATUS

approved



