A170837 a(0)=0, a(1)=1 and a(n) = 16n-27 for n >= 2.

0, 1, 5, 21, 37, 53, 69, 85, 101, 117, 133, 149, 165, 181, 197, 213, 229, 245, 261, 277, 293, 309, 325, 341, 357, 373, 389, 405, 421, 437, 453, 469, 485, 501, 517, 533, 549, 565, 581, 597, 613, 629, 645, 661, 677, 693, 709, 725, 741, 757, 773, 789, 805

Offset: 0

Author

N. J. A. Sloane, Jan 05 2010, based on email from R. J. Mathar and Benoit Jubin, Jun 02 2009; revised Jan 09 2010

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A170836 (first differences), A170876.

Programs

Magma

I:=[0, 1, 5, 21]; [n le 4 select I[n] else 2*Self(n-1) - Self(n-2): n in [1..60]]; // Vincenzo Librandi, Dec 19 2012

Mathematica

CoefficientList[Series[x*(3*x + 12*x^2 + 1)/(x - 1)^2, {x, 0, 60}], x] (* Vincenzo Librandi, Dec 19 2012 *)
LinearRecurrence[{2,-1},{0,1,5,21},60] (* Harvey P. Dale, Oct 09 2017 *)

Formula

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

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

a(n) = 4*A016813(n-2) + 1, n>=2. - Ivan N. Ianakiev, Jul 20 2013