A176662 a(0)=2, a(1)=7, and a(n) = (3*n+1)*2^(n-1) if n > 1.

2, 7, 14, 40, 104, 256, 608, 1408, 3200, 7168, 15872, 34816, 75776, 163840, 352256, 753664, 1605632, 3407872, 7208960, 15204352, 31981568, 67108864, 140509184, 293601280, 612368384, 1275068416, 2650800128, 5502926848, 11408506880, 23622320128, 48855252992

Offset: 0

Author

Paul Curtz, Apr 23 2010

Keywords

• nonn
• easy

Comments

The sequence appears on the main diagonal of the array defined by A123167 in the first row and successive differences in followup rows:

2, 3, 10, 7, 18, 11, 26, 15, 34, 19, ... A123167

1, 7, -3, 11, -7, 15, -11, 19, -15, 23, ... first diff

6, -10, 14, -18, 22 -26, 30, -34, 38, ... second diff

-16, 24, -32, 40, -48, 56, -64, 72, -80, ... third diff

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (4,-4).

Programs

Mathematica

LinearRecurrence[{4,-4},{2,7,14,40},40] (* or *) Join[{2,7},Table[ (3n+1) 2^(n-1),{n,2,40}]] (* Harvey P. Dale, Oct 05 2019 *)

Formula

a(n) mod 9 = A010710(n-1), n > 2.

a(2n) + a(2n+1) = 9, 54, 360, 2016, ...

a(n) - 2*a(n-1) = 12*A131577(n-2), n > 1.

a(n) = 4*a(n-1) - 4*a(n-2), n > 3.

G.f.: (-6*x^2+12*x^3+2-x)/(1-2*x)^2.

Extensions

Edited by R. J. Mathar, Jun 30 2010