The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A308767 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A308767

Number of partitions of n into 4 squarefree parts.
(history; published version)

#9 by Susanna Cuyler at Tue Jun 25 03:59:50 EDT 2019

STATUS

proposed

approved

#8 by Wesley Ivan Hurt at Mon Jun 24 21:50:04 EDT 2019

STATUS

editing

proposed

#7 by Wesley Ivan Hurt at Mon Jun 24 21:41:27 EDT 2019

FORMULA

a(n) = A308783(n)/n.

CROSSREFS

Cf. A008683, A308783.

#6 by Wesley Ivan Hurt at Mon Jun 24 04:07:20 EDT 2019

FORMULA

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

#5 by Wesley Ivan Hurt at Sun Jun 23 21:29:13 EDT 2019

STATUS

proposed

editing

#4 by Wesley Ivan Hurt at Sun Jun 23 14:00:20 EDT 2019

STATUS

editing

proposed

#3 by Wesley Ivan Hurt at Sun Jun 23 13:13:51 EDT 2019

NAME

allocated for Wesley Ivan HurtNumber of partitions of n into 4 squarefree parts.

DATA

0, 0, 0, 0, 1, 1, 2, 2, 4, 4, 6, 6, 8, 8, 11, 11, 15, 15, 19, 20, 25, 24, 30, 30, 37, 36, 44, 43, 53, 52, 60, 60, 71, 69, 80, 80, 93, 92, 106, 104, 122, 119, 135, 134, 155, 152, 172, 172, 194, 192, 213, 212, 239, 234, 257, 256, 290, 281, 308, 305, 343, 336

OFFSET

0,7

LINKS

<a href="/index/Par#part">Index entries for sequences related to partitions</a>

FORMULA

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

MATHEMATICA

Table[Sum[Sum[Sum[MoebiusMu[k]^2*MoebiusMu[j]^2*MoebiusMu[i]^2*MoebiusMu[n - i - j - k]^2, {i, j, Floor[(n - j - k)/2]}], {j, k, Floor[(n - k)/3]}], {k, Floor[n/4]}], {n, 0, 100}]

CROSSREFS

Cf. A008683.

KEYWORD

allocated

nonn

AUTHOR

Wesley Ivan Hurt, Jun 23 2019

STATUS

approved

editing

#2 by Wesley Ivan Hurt at Sun Jun 23 13:13:51 EDT 2019

NAME

allocated for Wesley Ivan Hurt

KEYWORD

recycled

allocated

#1 by Russ Cox at Sun Jan 27 08:30:53 EST 2019

KEYWORD

recycled

STATUS

approved