The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A157257 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A157257

Positive numbers y such that y^2 is of the form x^2+(x+41)^2 with integer x.
(history; published version)

#11 by Charles R Greathouse IV at Thu Sep 08 08:45:41 EDT 2022

PROG

(MAGMAMagma) Q:=Rationals(); R<x>:=PowerSeriesRing(Q, 40); Coefficients(R!((1-x)*(29+70*x+155*x^2+70*x^3+29*x^4)/(1-6*x^3+ x^6))) // G. C. Greubel, Feb 04 2018

Discussion

Thu Sep 08

08:45

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

#10 by Bruno Berselli at Mon Feb 05 02:56:54 EST 2018

STATUS

reviewed

approved

#9 by Paolo P. Lava at Mon Feb 05 02:26:39 EST 2018

STATUS

proposed

reviewed

#8 by G. C. Greubel at Sun Feb 04 23:28:18 EST 2018

STATUS

editing

proposed

#7 by G. C. Greubel at Sun Feb 04 23:28:10 EST 2018

LINKS

G. C. Greubel, <a href="/A157257/b157257.txt">Table of n, a(n) for n = 1..1001</a>

<a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,6,0,0,-1).

FORMULA

a(n) = 6*a(n-3) - a(n-6) for n > 6; a(1)=29, a(2)=41, a(3)=85, a(4)=89, a(5)=205, a(6)=481.

MATHEMATICA

CoefficientList[Series[(1-x)*(29+70*x+155*x^2+70*x^3+29*x^4)/(1-6*x^3+ x^6), {x, 0, 50}], x] (* G. C. Greubel, Feb 04 2018 *)

PROG

(PARI) x='x+O('x^30); Vec((1-x)*(29+70*x+155*x^2+70*x^3+29*x^4)/(1-6*x^3+ x^6)) \\ G. C. Greubel, Feb 04 2018

(MAGMA) Q:=Rationals(); R<x>:=PowerSeriesRing(Q, 40); Coefficients(R!((1-x)*(29+70*x+155*x^2+70*x^3+29*x^4)/(1-6*x^3+ x^6))) // G. C. Greubel, Feb 04 2018

STATUS

approved

editing

#6 by Charles R Greathouse IV at Sat Jun 13 00:53:01 EDT 2015

LINKS

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

Discussion

Sat Jun 13

00:53

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

#5 by Charles R Greathouse IV at Fri Jun 12 15:26:57 EDT 2015

LINKS

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

Discussion

Fri Jun 12

15:26

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

#4 by Russ Cox at Fri Mar 30 17:28:00 EDT 2012

AUTHOR

_Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), _, Feb 26 2009

Discussion

Fri Mar 30

17:28

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

#3 by Charles R Greathouse IV at Wed Dec 28 10:27:56 EST 2011

STATUS

editing

approved

#2 by Charles R Greathouse IV at Wed Dec 28 10:27:53 EST 2011

LINKS

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

KEYWORD

nonn,easy

STATUS

approved

editing