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A094572 Number of pairs of integers x, y (of either sign) with x^2 - y^2 = n. +0
1
2, 0, 4, 2, 4, 0, 4, 4, 6, 0, 4, 4, 4, 0, 8, 6, 4, 0, 4, 4, 8, 0, 4, 8, 6, 0, 8, 4, 4, 0, 4, 8, 8, 0, 8, 6, 4, 0, 8, 8, 4, 0, 4, 4, 12, 0, 4, 12, 6, 0, 8, 4, 4, 0, 8, 8, 8, 0, 4, 8, 4, 0, 12, 10, 8, 0, 4, 4, 8, 0, 4, 12, 4, 0, 12, 4, 8, 0, 4, 12, 10, 0, 4, 8, 8, 0, 8, 8, 4, 0, 8, 4, 8, 0, 8, 16, 4, 0, 12, 6 (list; graph; listen)
OFFSET

1,1

COMMENT

The old entry with this sequence number was a duplicate of A058071.

REFERENCES

M. N. Huxley, Area, Lattice Points and Exponential Sums, Oxford, 1996; p. 236.

FORMULA

a(n) = 2d(n) if n is odd, = 2d(n/4) if n == 0 mod 4, otherwise 0, where d() = A000005().

MAPLE

with(numtheory); f:=proc(n) if n mod 2 = 1 then RETURN(2*tau(n)); fi; if n mod 4 = 0 then RETURN(2*tau(n/4)); fi; 0; end;

CROSSREFS

Cf. A000005, A093061.

Sequence in context: A155984 A028609 A107490 this_sequence A079534 A097042 A097945

Adjacent sequences: A094569 A094570 A094571 this_sequence A094573 A094574 A094575

KEYWORD

nonn

AUTHOR

N. J. A. Sloane (njas(AT)research.att.com), Nov 02 2008

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Last modified December 2 11:54 EST 2009. Contains 167921 sequences.


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