The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A157288 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A157288

a(n) = 10368*n^2 - 288*n + 1.
(history; published version)

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

PROG

(MAGMAMagma) I:=[10081, 40897, 92449]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]]; // Vincenzo Librandi, Jan 28 2012

Discussion

Thu Sep 08

08:45

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

#18 by Giovanni Resta at Sun Aug 19 02:30:05 EDT 2018

STATUS

reviewed

approved

#17 by Michel Marcus at Sun Aug 19 01:32:20 EDT 2018

STATUS

proposed

reviewed

#16 by Jon E. Schoenfield at Sun Aug 19 01:25:57 EDT 2018

STATUS

editing

proposed

#15 by Jon E. Schoenfield at Sun Aug 19 01:25:55 EDT 2018

NAME

10368na(n) = 10368*n^2 - 288n 288*n + 1.

COMMENTS

The identity (10368*n^2 - 288*n + 1)^2 - (36*n^2 - n)*(1728*n - 24)^2 = 1 can be written as a(n)^2 - A157286(n)*A157287(n)^2 = 1 (see also second part of the comment in at A157286). - _Vincenzo Librandi, _, Jan 28 2012

FORMULA

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - _Vincenzo Librandi, _, Jan 28 2012

G.f.: x*(-10081 - 10654*x - x^2)/(x-1)^3. - _Vincenzo Librandi, _, Jan 28 2012

PROG

(MAGMA) I:=[10081, 40897, 92449]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]]; // _Vincenzo Librandi, _, Jan 28 2012

(PARI) for(n=1, 40, print1(10368*n^2 - 288*n + 1", ")); \\ _Vincenzo Librandi, _, Jan 28 2012

STATUS

approved

editing

#14 by Charles R Greathouse IV at Sat Jun 17 02:52:32 EDT 2017

LINKS

<a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).

Discussion

Sat Jun 17

02:52

OEIS Server: https://oeis.org/edit/global/2661

#13 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 (3,-3,1).

Discussion

Sat Jun 13

00:53

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

#12 by Charles R Greathouse IV at Fri Jun 12 15:32:45 EDT 2015

LINKS

<a href="/index/Rec#recLCC">Index to sequences with linear recurrences with constant coefficients</a>, signature (3,-3,1).

Discussion

Fri Jun 12

15:32

OEIS Server: https://oeis.org/edit/global/2437

#11 by Charles R Greathouse IV at Fri Jun 12 15:19:02 EDT 2015

LINKS

<a href="/Sindx_Rea.htmlindex/Rec#recLCC">Index to sequences with linear recurrences with constant coefficients</a>, signature (3,-3,1).

Discussion

Fri Jun 12

15:19

OEIS Server: https://oeis.org/edit/global/2434

#10 by Charles R Greathouse IV at Sun Aug 03 14:26:19 EDT 2014

MATHEMATICA

LinearRecurrence[{3, -3, 1}, {10081, 40897, 92449}, 40] (* _Vincenzo Librandi, _, Jan 28 2012 *)

Discussion

Sun Aug 03

14:26

OEIS Server: https://oeis.org/edit/global/2270