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A092362
Number of partitions of n^2 into squares greater than 1.
7
1, 0, 1, 1, 2, 3, 5, 8, 11, 28, 44, 94, 167, 354, 643, 1314, 2412, 4792, 8981, 17374, 32566, 62008, 115702, 217040, 402396, 745795, 1372266, 2517983, 4595652, 8354350, 15125316, 27265107, 48972467, 87584837, 156119631, 277152178, 490437445, 864534950
OFFSET
0,5
COMMENTS
a(n) = A078134(A000290(n)).
LINKS
FORMULA
a(n) ~ exp(3*Pi^(1/3) * Zeta(3/2)^(2/3) * n^(2/3) / 2^(4/3)) * Zeta(3/2)^(4/3) / (2^(11/3) * sqrt(3) * Pi^(5/6) * n^(11/3)). - Vaclav Kotesovec, Apr 10 2017
EXAMPLE
a(6) = 5: 6^2 = 36 = 16+16+4 = 16+4+4+4+4+4 = 9+9+9+9 = 4+4+4+4+4+4+4+4+4.
MAPLE
b:=proc(n, i) option remember; `if`(n=0, 1,
`if`(i<2, 0, b(n, i-1) +`if`(i^2>n, 0, b(n-i^2, i))))
end:
a:= n-> b(n^2, n):
seq(a(n), n=0..50); # Alois P. Heinz, Apr 15 2013
MATHEMATICA
b[n_, i_] := b[n, i] = If[n == 0, 1, If[i<2, 0, b[n, i-1] + If[i^2>n, 0, b[n-i^2, i]]]]; a[n_] := b[n^2, n]; Table[a[n], {n, 0, 50}] (* Jean-François Alcover, Nov 11 2015, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Mar 19 2004
EXTENSIONS
Corrected a(0) and more terms from Alois P. Heinz, Apr 15 2013
STATUS
approved