login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A139271 a(n) = 2*n*(4*n-3). 16
0, 2, 20, 54, 104, 170, 252, 350, 464, 594, 740, 902, 1080, 1274, 1484, 1710, 1952, 2210, 2484, 2774, 3080, 3402, 3740, 4094, 4464, 4850, 5252, 5670, 6104, 6554, 7020, 7502, 8000, 8514, 9044, 9590, 10152, 10730, 11324, 11934, 12560 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Sequence found by reading the line from 0, in the direction 0, 2, ..., in the square spiral whose vertices are the triangular numbers A000217. Opposite numbers to the members of A033585 in the same spiral.

Twice decagonal numbers (or twice 10-gonal numbers). - Omar E. Pol, May 15 2008

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..5000

Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos.

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

FORMULA

a(n) = 8*n^2 - 6*n.

Sequences of the form a(n) = 8*n^2 + c*n have generating functions x{c+8+(8-c)x} / (1-x)^3 and recurrence a(n) = 3a(n-1) - 3a(n-2) + a(n-3). The inverse binomial transform is 0, c+8, 16, 0, 0, ... (0 continued). This applies to A139271-A139278, positive or negative c. - R. J. Mathar, May 12 2008

a(n) = A001107(n)*2. - Omar E. Pol, May 15 2008

a(n) = 16*n + a(n-1) - 14 (with a(0)=0). - Vincenzo Librandi, Aug 03 2010

From G. C. Greubel, Jul 18 2017: (start)

G.f.: (2*x)*(7*x+1)/(1-x)^3.

E.g.f.: (8*x^2 + 2*x)*exp(x). (End)

MATHEMATICA

s=0; lst={s}; Do[s+=n; AppendTo[lst, s], {n, 2, 6!, 16}]; lst (* Vladimir Joseph Stephan Orlovsky, Apr 02 2009 *)

Table[8n^2-6n, {n, 0, 40}] (* or *) LinearRecurrence[{3, -3, 1}, {0, 2, 20}, 50] (* Harvey P. Dale, Sep 26 2016 *)

PROG

(PARI) a(n)=2*n*(4*n-3) \\ Charles R Greathouse IV, Jun 17 2017

CROSSREFS

Cf. A000217, A014634, A014635, A033585, A033586, A033587, A035008, A051870, A069129, A085250, A139272, A139273, A139274, A139275, A139276, A139278, A139279, A139280, A139281, A139282.

Cf. A001107.

Cf. numbers of the form n*(n*k-k+4))/2 listed in A226488 (this sequence is the case k=16). - Bruno Berselli, Jun 10 2013

Sequence in context: A261838 A225065 A059211 * A133217 A001504 A192351

Adjacent sequences:  A139268 A139269 A139270 * A139272 A139273 A139274

KEYWORD

easy,nonn

AUTHOR

Omar E. Pol, Apr 26 2008

EXTENSIONS

Corrected by Harvey P. Dale, Sep 26 2016

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 14 14:50 EST 2019. Contains 329979 sequences. (Running on oeis4.)