The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A016778 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A016778

a(n) = (3*n+1)^2.
(history; published version)

#55 by Michel Marcus at Thu Nov 12 10:34:32 EST 2020

STATUS

reviewed

approved

#54 by Joerg Arndt at Thu Nov 12 10:11:14 EST 2020

STATUS

proposed

reviewed

#53 by Michel Marcus at Thu Nov 12 03:39:51 EST 2020

STATUS

editing

proposed

#52 by Michel Marcus at Thu Nov 12 03:39:48 EST 2020

LINKS

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

STATUS

proposed

editing

#51 by Amiram Eldar at Thu Nov 12 03:37:34 EST 2020

STATUS

editing

proposed

#50 by Amiram Eldar at Thu Nov 12 03:11:56 EST 2020

FORMULA

From Amiram Eldar, Nov 12 2020: (Start)

Sum_{n>=0} 1/a(n) = A214550.

Sum_{n>=0} (-1)^n/a(n) = A262178. (End)

CROSSREFS

Cf. A000212, A214550, A262178.

STATUS

approved

editing

#49 by Michel Marcus at Sun Mar 31 05:00:43 EDT 2019

STATUS

reviewed

approved

#48 by Joerg Arndt at Sun Mar 31 02:23:42 EDT 2019

STATUS

proposed

reviewed

#47 by Jon E. Schoenfield at Fri Mar 29 21:55:54 EDT 2019

STATUS

editing

proposed

Discussion

Sat Mar 30

03:55

Paul Curtz: Jon, Yes. Thank you very much.

#46 by Jon E. Schoenfield at Fri Mar 29 21:55:08 EDT 2019

COMMENTS

From Paul Curtz, Mar 28 2019 : (Start)

Sequence is a spoke of the hexagonal spiral built with from the terms of A016777:

.

\

100 --97 --94 --91

\ \

49 --46 --43 88

/ \ \ \

52 16 --13 40 85

/ / \ \ \ \

/ / / / / /

58 22 4 ---7 34 79

\ \ / /

61 25 --28 --31 76

\ /

64 --67 --70 --73

FORMULA

a(n) = a(n-1) + 3*(6*n-1) (with ; a(0)=1). [_- _Vincenzo Librandi_, Nov 20 2010]

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3), with ; a(0)=1, a(1)=16, a(2)=49. - Harvey P. Dale, Mar 03 2013

AUTHOR

N. J. A. Sloane.

STATUS

proposed

editing

Discussion

Fri Mar 29

21:55

Jon E. Schoenfield: @Paul -- are these changes to the hexagonal spiral okay with you?