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A156159 Squares of the form k^2+(k+17)^2 with integer k. 4
169, 289, 625, 2809, 7225, 18769, 93025, 243049, 635209, 3157729, 8254129, 21576025, 107267449, 280395025, 732947329, 3643933225, 9525174409, 24898630849, 123786459889, 323575532569, 845820499225, 4205095700689 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Square roots of k^2+(k+17)^2 are in A155923, values k (except for -5) are in A118120.

lim_{n -> infinity} a(n)/a(n-3) = (17+12*sqrt(2)).

lim_{n -> infinity} a(n)/a(n-1) = ((19+6*sqrt(2))/17)^2 for n mod 3 = {0, 2}.

lim_{n -> infinity} a(n)/a(n-1) = ((387+182*sqrt(2))/17^2)^2 for n mod 3 = 1.

LINKS

Table of n, a(n) for n=1..22.

Index entries for linear recurrences with constant coefficients, signature (1,0,34,-34,0,-1,1).

FORMULA

a(n) = 34*a(n-3)-a(n-6)-2312 for n > 6; a(1)=169, a(2)=289, a(3)=625, a(4)=2809, a(5)=7225, a(6)=18769.

G.f.: x*(169+120*x+336*x^2-3562*x^3+336*x^4+120*x^5+169*x^6)/((1-x)*(1-34*x^3+x^6)).

EXAMPLE

625 = 25^2 is of the form k^2+(k+17)^2 with k = 7: 7^2+24^2 = 625. Hence 625 is in the sequence.

PROG

(PARI) {forstep(n=-5, 1600000, [1, 3], if(issquare(a=2*n*(n+17)+289), print1(a, ", ")))}

CROSSREFS

Equals A155923^2. Cf. A156160 (first trisection), A156161 (second trisection), A156162 (third trisection).

Cf. A118120, A156035 (decimal expansion of 3+2*sqrt(2)), A156164 (decimal expansion of 17+12*sqrt(2)), A156163 (decimal expansion of (19+6*sqrt(2))/17), A157649 (decimal expansion of (387+182*sqrt(2))/17^2).

Sequence in context: A287391 A325421 A296304 * A099011 A330276 A327652

Adjacent sequences:  A156156 A156157 A156158 * A156160 A156161 A156162

KEYWORD

nonn,easy

AUTHOR

Klaus Brockhaus, Feb 09 2009

EXTENSIONS

G.f. corrected, fourth comment and cross-references edited by Klaus Brockhaus, Sep 23 2009

STATUS

approved

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Last modified April 6 10:47 EDT 2020. Contains 333273 sequences. (Running on oeis4.)