login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A159701 Positive numbers y such that y^2 is of the form x^2+(x+967)^2 with integer x. 4
925, 967, 1013, 4537, 4835, 5153, 26297, 28043, 29905, 153245, 163423, 174277, 893173, 952495, 1015757, 5205793, 5551547, 5920265, 30341585, 32356787, 34505833, 176843717, 188589175, 201114733, 1030720717, 1099178263 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

(-43, a(1)) and (A130017(n), a(n+1)) are solutions (x, y) to the Diophantine equation x^2+(x+967)^2 = y^2.

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

Lim_{n -> infinity} a(n)/a(n-1) = (969+44*sqrt(2))/967 for n mod 3 = {0, 2}.

Lim_{n -> infinity} a(n)/a(n-1) = (2487411+1629850*sqrt(2))/967^2 for n mod 3 = 1.

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..3895

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

FORMULA

a(n) = 6*a(n-3) - a(n-6) for n > 6; a(1)=925, a(2)=967, a(3)=1013, a(4)=4537, a(5)=4835, a(6)=5153.

G.f.: (1-x)*(925+1892*x+2905*x^2+1892*x^3+925*x^4) / (1-6*x^3+x^6).

a(3*k-1) = 967*A001653(k) for k >= 1.

EXAMPLE

(-43, a(1)) = (-43, 925) is a solution: (-43)^2+(-43+967)^2 = 1849+853776 = 855625 = 925^2.

(A130017(1), a(2)) = (0, 967) is a solution: 0^2+(0+967)^2 = 935089 = 967^2.

(A130017(3), a(4)) = (2688, 4537) is a solution: 2688^2+(2688+967)^2 = 7225344+13359025 = 20584369 = 4537^2.

MATHEMATICA

LinearRecurrence[{0, 0, 6, 0, 0, -1}, {925, 967, 1013, 4537, 4835, 5153}, 40] (* G. C. Greubel, May 22 2018 *)

PROG

(PARI) {forstep(n=-44, 10000000, [1, 3], if(issquare(2*n^2+1934*n+935089, &k), print1(k, ", ")))};

(PARI) x='x+O('x^30); Vec((1-x)*(925+1892*x+2905*x^2+1892*x^3+925*x^4)/( 1-6*x^3+x^6)) \\ G. C. Greubel, May 22 2018

(MAGMA) I:=[925, 967, 1013, 4537, 4835, 5153]; [n le 6 select I[n] else 6*Self(n-3) - Self(n-6): n in [1..30]]; // G. C. Greubel, May 22 2018

CROSSREFS

Cf. A130017, A001653, A156035 (decimal expansion of 3+2*sqrt(2)), A159702 (decimal expansion of (969+44*sqrt(2))/967), A159703 (decimal expansion of (2487411+1629850*sqrt(2))/967^2).

Sequence in context: A172880 A172912 A172702 * A115696 A066741 A325141

Adjacent sequences:  A159698 A159699 A159700 * A159702 A159703 A159704

KEYWORD

nonn,easy

AUTHOR

Klaus Brockhaus, Apr 21 2009

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 21 01:08 EDT 2021. Contains 345337 sequences. (Running on oeis4.)