A169724 (2*3^(n-1)+1)^2.

9, 49, 361, 3025, 26569, 237169, 2128681, 19140625, 172213129, 1549760689, 13947373801, 125524947025, 1129720271689, 10167469690609, 91507188951721, 823564585774225, 7412080927594249, 66708727315226929, 600378542737678441, 5403406875341014225

Offset: 1

Author

Alice V. Kleeva (alice27353(AT)gmail.com), Jan 19 2010

Keywords

• nonn
• easy

Comments

A subsequence of the squares A000290.

Essentially equal to A052919(n)^2.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Alice V. Kleeva, Grid for this sequence
• Alice V. Kleeva, Illustration of initial terms
• Robert Munafo, Sequence A169720, and two others by Alice V. Kleeva
• Robert Munafo, Sequence A169720, and two others by Alice V. Kleeva [Cached copy, in pdf format, included with permission]
• Index entries for linear recurrences with constant coefficients, signature (13,-39,27).

Crossrefs

Cf. A169720-A169727, A100702.

Programs

Magma

I:=[9, 49, 361]; [n le 3 select I[n] else 13*Self(n-1) - 39*Self(n-2) + 27*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Dec 03 2012

Mathematica

CoefficientList[Series[(-9 + 68 x - 75 x^2)/((x - 1) (3 x - 1) (9 x - 1)), {x, 0, 40}], x] (* Vincenzo Librandi, Dec 03 2012 *)
LinearRecurrence[{13,-39,27},{9,49,361},20] (* Harvey P. Dale, Apr 23 2024 *)

Formula

a(n)= +13*a(n-1) -39*a(n-2) +27*a(n-3). G.f.: x*( -9+68*x-75*x^2 ) / ( (x-1)*(3*x-1)*(9*x-1) ). [R. J. Mathar, Apr 26 2010]

Extensions

G.f. adapted to the offset by Vincenzo Librandi, Dec 03 2012