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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A152760 4 times 9-gonal numbers: a(n) = 2*n*(7*n-5). 10
0, 4, 36, 96, 184, 300, 444, 616, 816, 1044, 1300, 1584, 1896, 2236, 2604, 3000, 3424, 3876, 4356, 4864, 5400, 5964, 6556, 7176, 7824, 8500, 9204, 9936, 10696, 11484, 12300, 13144, 14016, 14916, 15844, 16800, 17784, 18796, 19836, 20904, 22000, 23124 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Sequence found by reading the line from 0, in the direction 0, 4, ..., in the Pythagorean spiral whose edges have length A195019 and whose vertices are the numbers A195020. The square spiral is related to the primitive Pythagorean triple [3, 4, 5]. - Omar E. Pol, Oct 13 2011

LINKS

Table of n, a(n) for n=0..41.

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

FORMULA

a(n) = 14n^2 - 10n = A001106(n)*4 = A139268(n)*2.

a(n) = a(n-1) + 28*n - 24 (with a(0)=0). - Vincenzo Librandi, Nov 26 2010

From Colin Barker, Apr 09 2012: (Start)

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).

G.f.: 4*x*(1+6*x)/(1-x)^3. (End)

MATHEMATICA

s=0; lst={s}; Do[s+=n; AppendTo[lst, s], {n, 4, 8!, 28}]; lst (* Vladimir Joseph Stephan Orlovsky, Apr 02 2009 *)

4*PolygonalNumber[9, Range[0, 50]] (* Requires Mathematica version 10 or later *) (* or *) LinearRecurrence[{3, -3, 1}, {0, 4, 36}, 50] (* Harvey P. Dale, Aug 26 2019 *)

PROG

(PARI) a(n)=2*n*(7*n-5) \\ Charles R Greathouse IV, Oct 07 2015

CROSSREFS

Cf. A001106, A139268, A152759.

Sequence in context: A075215 A193833 A193183 * A016826 A190318 A193874

Adjacent sequences:  A152757 A152758 A152759 * A152761 A152762 A152763

KEYWORD

easy,nonn

AUTHOR

Omar E. Pol, Dec 14 2008

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 November 20 14:54 EST 2019. Contains 329337 sequences. (Running on oeis4.)