A130014 Nonnegative values x of solutions (x, y) to the Diophantine equation x^2+(x+881)^2 = y^2.

0, 43, 2440, 2643, 2860, 16443, 17620, 18879, 97980, 104839, 112176, 573199, 613176, 655939, 3342976, 3575979, 3825220, 19486419, 20844460, 22297143, 113577300, 121492543, 129959400, 661979143, 708112560, 757461019, 3858299320

Offset

1,2

Comments

Also values x of Pythagorean triples (x, x+881, y).

Corresponding values y of solutions (x, y) are in A159690.

For the generic case x^2+(x+p)^2 = y^2 with p = 2*m^2-1 a (prime) number in A066436 see A118673 or A129836.

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

lim_{n -> infinity} a(n)/a(n-1) = (883+42*sqrt(2))/881 for n mod 3 = {1, 2}.

lim_{n -> infinity} a(n)/a(n-1) = (2052963+1343918*sqrt(2))/881^2 for n mod 3 = 0.

Links

Table of n, a(n) for n=1..27.

Index entries for linear recurrences with constant coefficients, signature (1,0,6,-6,0,-1,1).

Formula

a(n) = 6*a(n-3)-a(n-6)+1762 for n > 6; a(1)=0, a(2)=43, a(3)=2440, a(4)=2643, a(5)=2860, a(6)=16443.

G.f.: x*(43+2397*x+203*x^2-41*x^3-799*x^4-41*x^5) / ((1-x)*(1-6*x^3+x^6)).

a(3*k+1) = 881*A001652(k) for k >= 0.

Mathematica

LinearRecurrence[{1, 0, 6, -6, 0, -1, 1}, {0, 43, 2440, 2643, 2860, 16443, 17620}, 30] (* Harvey P. Dale, Aug 13 2015 *)

Prog

(PARI) {forstep(n=0, 10000000, [1, 3], if(issquare(2*n^2+1762*n+776161), print1(n, ", ")))}

Crossrefs

Cf. A159690, A066436, A118673, A118674, A129836, A001652, A156035 (decimal expansion of 3+2*sqrt(2)), A159691 (decimal expansion of (883+42*sqrt(2))/881), A159692 (decimal expansion of (2052963+1343918*sqrt(2))/881^2).

Sequence in context: A335207 A076572 A015258 * A246535 A265234 A357557

Adjacent sequences: A130011 A130012 A130013 * A130015 A130016 A130017

Keyword

nonn,easy

Author

Mohamed Bouhamida, Jun 15 2007

Extensions

Edited and two terms added by Klaus Brockhaus, Apr 21 2009

Status

approved