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Revision History for A160739

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A160739

16*P_6(n), 16 times the Legendre Polynomial of order 6 at n.
(history; published version)

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

PROG

(MAGMAMagma) [231*n^6 -315*n^4 +105*n^2 -5: n in [0..30]]; // G. C. Greubel, May 02 2018

Discussion

Thu Sep 08

08:45

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

#25 by Alois P. Heinz at Tue Jul 23 09:03:44 EDT 2019

STATUS

proposed

approved

#24 by Colin Barker at Tue Jul 23 08:06:18 EDT 2019

STATUS

editing

proposed

#23 by Colin Barker at Tue Jul 23 08:05:44 EDT 2019

LINKS

<a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7, -21, 35, -35, 21, -7, 1).

FORMULA

a(n) = 231*n^6 - 315*n^4 + 105*n^2 - 5. - Vaclav Kotesovec, Jul 31 2013

From Colin Barker, Jul 23 2019: (Start)

G.f.: -(5 - 51*x - 9942*x^2 - 73222*x^3 - 73047*x^4 - 10047*x^5 - 16*x^6) / (1 - x)^7.

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>6.

(End)

PROG

(PARI) Vec(-(5 - 51*x - 9942*x^2 - 73222*x^3 - 73047*x^4 - 10047*x^5 - 16*x^6) / (1 - x)^7 + O(x^30)) \\ Colin Barker, Jul 23 2019

STATUS

approved

editing

#22 by Bruno Berselli at Thu May 03 03:03:58 EDT 2018

STATUS

reviewed

approved

#21 by Michel Marcus at Thu May 03 00:59:58 EDT 2018

STATUS

proposed

reviewed

Discussion

Thu May 03

01:34

G. C. Greubel: About a year or more ago a discussion circulated about spaces and their relations to separation of powers and next term indicators (+/-). From then a space was added for clarity. Recently it seems its reverting back to jamming all the terms together.

#20 by G. C. Greubel at Thu May 03 00:58:01 EDT 2018

STATUS

editing

proposed

#19 by G. C. Greubel at Thu May 03 00:57:53 EDT 2018

FORMULA

a(n) = 231*n^6 -315*n^4 +105*n^2 -5. - Vaclav Kotesovec, Jul 31 2013

STATUS

reviewed

editing

#18 by Michel Marcus at Thu May 03 00:25:39 EDT 2018

STATUS

proposed

reviewed

#17 by G. C. Greubel at Wed May 02 23:37:11 EDT 2018

STATUS

editing

proposed

Discussion

Thu May 03

00:24

Michel Marcus: why change the way the formula was written ????