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A216283 Number of nonnegative solutions to the equation x^2+5*y^2 = n. 2
1, 0, 0, 1, 1, 1, 0, 0, 2, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 2, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 0, 0, 2, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 3, 0, 0, 2, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,9
COMMENTS
Records occur at 1, 9, 81, 189, 441, 1449, 3969, 12789, 13041, 30429, ... - Antti Karttunen, Aug 23 2017
LINKS
FORMULA
G.f. T(x) * T(x^5) where T(x) = sum(n>=0, x^(n^2) ). - Joerg Arndt, Sep 21 2012
EXAMPLE
For n = 9, there are two solutions: 9 = 3^2 + 5*(0^2) = 2^2 + 5*(1^2), thus a(9) = 2.
For n = 81, there are three solutions: 81 = 9^2 + 5*(0^2) = 6^2 + 5*(3^2) = 1^2 + 5*(4^2), thus a(81) = 3.
PROG
(PARI)
N=666; x='x+O('x^N);
T(x)=sum(n=0, ceil(sqrt(N)), x^(n*n));
Vec(T(x)*T(x^5))
/* Joerg Arndt, Sep 21 2012 */
(Scheme) (define (A216283 n) (cond ((< n 2) 1) (else (let loop ((k (A000196 n)) (s 0)) (if (< k 0) s (let ((x (- n (* k k)))) (loop (- k 1) (+ s (if (zero? (modulo x 5)) (A010052 (/ x 5)) 0))))))))) ;; Antti Karttunen, Aug 23 2017
CROSSREFS
Cf. A033718 (all solutions x^2+5*y^2 = n).
Cf. A020669 (positions of nonzeros).
Sequence in context: A277143 A239434 A033770 * A262900 A242830 A101668
KEYWORD
nonn
AUTHOR
V. Raman, Sep 03 2012
EXTENSIONS
Examples from Antti Karttunen, Aug 23 2017
STATUS
approved

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Last modified April 23 10:29 EDT 2024. Contains 371905 sequences. (Running on oeis4.)