A169726 a(n) = 3*2^n*(2^n-1) + 1.

1, 7, 37, 169, 721, 2977, 12097, 48769, 195841, 784897, 3142657, 12576769, 50319361, 201302017, 805257217, 3221127169, 12884705281, 51539214337, 206157643777, 824632147969, 3298531737601, 13194133241857, 52776545550337, 211106207367169, 844424879800321

Offset

0,2

Comments

A subsequence of the centered hexagonal numbers A003215.

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). - R. J. Mathar, Apr 26 2010

Formula

From R. J. Mathar, Apr 26 2010: (Start)

a(n) = 7*a(n-1) - 14*a(n-2) + 8*a(n-3).

G.f.: ( -1-2*x^2 ) / ( (x-1)*(2*x-1)*(4*x-1) ). (End)

a(n) = (2*A169720(n)+1)/3. - L. Edson Jeffery, Dec 03 2012

Maple

A169726:=n->3*2^n*(2^n-1)+1: seq(A169726(n), n=0..30); # Wesley Ivan Hurt, Sep 14 2014

Mathematica

CoefficientList[Series[(-1 - 2*x^2)/((x-1)*(2*x-1)*(4*x-1)), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 04 2012 *)
Table[c=2^n; 3c(c-1)+1, {n, 0, 30}] (* or *) LinearRecurrence[{7, -14, 8}, {1, 7, 37}, 30] (* Harvey P. Dale, Nov 22 2013 *)

Prog

(Magma) I:=[1, 7, 37]; [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
(Magma) [3*2^n*(2^n-1)+1 : n in [0..30]]; // Wesley Ivan Hurt, Sep 14 2014

Crossrefs

Cf. A000079, A003215, A169720-A169727.

Sequence in context: A049494 A049495 A169789 * A305781 A172063 A208737

Adjacent sequences: A169723 A169724 A169725 * A169727 A169728 A169729

Keyword

nonn,easy

Author

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

Status

approved