A152760 4 times 9-gonal numbers: a(n) = 2*n*(7*n-5).

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

Offset: 0

Author

Omar E. Pol, Dec 14 2008

Keywords

• easy
• nonn

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

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

Crossrefs

Cf. A001106, A139268, A152759, A195019, A195020, A195021.

Programs

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 *)

PARI

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

Formula

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

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)

From Elmo R. Oliveira, Dec 27 2024: (Start)

E.g.f.: 2*exp(x)*x*(2 + 7*x).

a(n) = n + A195021(n). (End)