The On-Line Encyclopedia of Integer Sequences (OEIS)

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A101152

Nonnegative values x of solutions (x, y) to the Diophantine equation x^2+(x+569)^2 = y^2.
(history; published version)

#16 by Charles R Greathouse IV at Thu Sep 08 08:45:16 EDT 2022

PROG

(MAGMAMagma) I:=[0, 111, 1260, 1707, 2280, 8791, 11380]; [n le 7 select I[n] else Self(n-1) +6*Self(n-3) -6*Self(n-4) -Self(n-6) +Self(n-7): n in [1..30]]; // G. C. Greubel, Apr 21 2018

Discussion

Thu Sep 08

08:45

OEIS Server: https://oeis.org/edit/global/2944

#15 by N. J. A. Sloane at Sat Feb 15 10:52:26 EST 2020

AUTHOR

_Mohamed Bouhamida (bhmd95(AT)yahoo.fr), _, Jun 03 2007

Discussion

Sat Feb 15

10:52

OEIS Server: https://oeis.org/edit/global/2849

#14 by Susanna Cuyler at Sat Apr 21 20:58:48 EDT 2018

STATUS

proposed

approved

#13 by G. C. Greubel at Sat Apr 21 19:08:18 EDT 2018

STATUS

editing

proposed

#12 by G. C. Greubel at Sat Apr 21 19:08:11 EDT 2018

LINKS

G. C. Greubel, <a href="/A101152/b101152.txt">Table of n, a(n) for n = 1..1000</a>

FORMULA

a(n) = 6*a(n-3) - a(n-6) + 1138 for n > 6; a(1)=0, a(2)=111, a(3)=1260, a(4)=1707, a(5)=2280, a(6)=8791.

G.f.: x*(111 +1149*x +447*x^2 -93*x^3 -383*x^4 -93*x^5) / ((1-x)*(1-6*x^3 +x^6)).

MATHEMATICA

LinearRecurrence[{1, 0, 6, -6, 0, -1, 1}, {0, 111, 1260, 1707, 2280, 8791, 11380}, 50] (* G. C. Greubel, Apr 21 2018 *)

PROG

(PARI) x='x+O('x^30); concat([0], Vec(x*(111 +1149*x +447*x^2 -93*x^3 -383*x^4 -93*x^5)/((1-x)*(1-6*x^3 +x^6)))) \\ G. C. Greubel, Apr 21 2018

(MAGMA) I:=[0, 111, 1260, 1707, 2280, 8791, 11380]; [n le 7 select I[n] else Self(n-1) +6*Self(n-3) -6*Self(n-4) -Self(n-6) +Self(n-7): n in [1..30]]; // G. C. Greubel, Apr 21 2018

STATUS

approved

editing

#11 by Charles R Greathouse IV at Sun Jun 18 02:25:43 EDT 2017

LINKS

<a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,6,-6,0,-1,1).

Discussion

Sun Jun 18

02:25

OEIS Server: https://oeis.org/edit/global/2678

#10 by Charles R Greathouse IV at Sat Jun 13 00:51:37 EDT 2015

LINKS

<a href="/index/Rec">Index to sequences with entries for linear recurrences with constant coefficients</a>, signature (1,0,6,-6,0,-1,1).

Discussion

Sat Jun 13

00:51

OEIS Server: https://oeis.org/edit/global/2439

#9 by Charles R Greathouse IV at Fri Jun 12 15:25:48 EDT 2015

LINKS

<a href="/index/Rea#recLCCRec">Index to sequences with linear recurrences with constant coefficients</a>, signature (1,0,6,-6,0,-1,1).

Discussion

Fri Jun 12

15:25

OEIS Server: https://oeis.org/edit/global/2436

#8 by Russ Cox at Fri Mar 30 17:27:45 EDT 2012

EXTENSIONS

Edited and two terms added by _Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), _, May 04 2009

Discussion

Fri Mar 30

17:27

OEIS Server: https://oeis.org/edit/global/145

#7 by Charles R Greathouse IV at Wed Dec 28 10:33:34 EST 2011

STATUS

editing

approved