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

Author

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

Keywords

• nonn
• easy

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

Crossrefs

Cf. A000079, A003215, A169720-A169727.

Programs

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

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 *)

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