A053730 a(n) = 2^(n-2)*(n^2 - n + 4).

1, 2, 6, 20, 64, 192, 544, 1472, 3840, 9728, 24064, 58368, 139264, 327680, 761856, 1753088, 3997696, 9043968, 20316160, 45350912, 100663296, 222298112, 488636416, 1069547520, 2332033024, 5066719232, 10972299264, 23689428992

Offset: 0

Author

N. J. A. Sloane, Mar 24 2000

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (6,-12,8).

Crossrefs

Cf. A053545.

Programs

GAP

List([0..30], n-> 2^(n-2)*(n^2 -n +4)); # G. C. Greubel, Sep 06 2019

Magma

I:=[1, 2, 6]; [n le 3 select I[n] else 6*Self(n-1)-12*Self(n-2) +8*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Apr 28 2012

Maple

seq(2^(n-2)*(n^2 -n +4), n=0..30); # G. C. Greubel, Sep 06 2019

Mathematica

CoefficientList[Series[(1-4*x+6*x^2)/(1-2*x)^3,{x,0,30}],x] (* Vincenzo Librandi, Apr 28 2012 *)
LinearRecurrence[{6,-12,8}, {1,2,6}, 30] (* G. C. Greubel, Sep 06 2019 *)

PARI

vector(30, n, 2^(n-3)*(n^2 -3*n +6)) \\ G. C. Greubel, Sep 06 2019

Sage

[2^(n-2)*(n^2 -n +4) for n in (0..30)] # G. C. Greubel, Sep 06 2019

Formula

G.f.: (1-4*x+6*x^2)/(1-2*x)^3. - Colin Barker, Apr 01 2012

a(n) = 6*a(n-1) - 12*a(n-2) + 8*a(n-3). - Vincenzo Librandi, Apr 28 2012

a(n) = Sum_{k=0..n} binomial(n,k) * A077028(n,k), where A077028(n,k) = (n-k)*k + 1. - Paul D. Hanna, Oct 11 2015