A169721 a(n) = (2*(3*2^(n-1)-1))^2.

1, 16, 100, 484, 2116, 8836, 36100, 145924, 586756, 2353156, 9424900, 37724164, 150945796, 603881476, 2415722500, 9663283204, 38653919236, 154617249796, 618472144900, 2473894871044, 9895592067076, 39582393434116, 158329624068100, 633318596935684

Offset: 0

Author

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

Keywords

• nonn
• easy

Comments

A subsequence of the squares (A000290).

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..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 (7,-14,8).

Crossrefs

Cf. A169720-A169727.

Programs

Magma

I:=[1,16,100]; [n le 3 select I[n] else 7*Self(n-1)-14*Self(n-2)+8*Self(n-3): n in [1..30]];// Vincenzo Librandi, Dec 04 2012

Mathematica

Table[(2(3*2^(n-1)-1))^2,{n,0,30}] (* Harvey P. Dale, Oct 29 2012 *)
CoefficientList[Series[(1+x)/((1-x)*(1-2*x)), {x, 0, 30}], x]^2 (* Vincenzo Librandi, Dec 04 2012 *)

Formula

a(n) = A033484(n)^2.

G.f.: (1+9*x+2*x^2)/(1-7*x+14*x^2-8*x^3). - Bruno Berselli, Dec 04 2012

a(n) = 7*a(n-1)-14*a(n-2)+8*a(n-3). - Vincenzo Librandi, Dec 04 2012