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A239434 Number of nonnegative integer solutions to the equation x^2 - 25*y^2 = n. 2
1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,64

COMMENTS

For (x, y) to be a solution to the more general equation x^2 - d^2*y^2 = n, it can be shown that n-f^2 must be divisible by 2*f*d, where f is a divisor of n not exceeding sqrt(n). Then y = (n-f^2)/(2*f*d) and x = d*y+f.

LINKS

Colin Barker, Table of n, a(n) for n = 1..1000

EXAMPLE

a(64)=2 because x^2 - 25*y^2 = 64 has two solutions, (X,Y) = (8,0) and (17,3).

PROG

(PARI) a(n) = sumdiv(n, f, f^2<=n && (n-f^2)%(10*f)==0)

CROSSREFS

Cf. A034178, A230240, A230263, A230264, A239435.

Sequence in context: A291147 A278929 A277143 * A033770 A216283 A262900

Adjacent sequences:  A239431 A239432 A239433 * A239435 A239436 A239437

KEYWORD

nonn

AUTHOR

Colin Barker, Mar 18 2014

STATUS

approved

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Last modified September 16 18:56 EDT 2019. Contains 327117 sequences. (Running on oeis4.)