A169727 a(n) = 3*(2^(n+1)-2)*(2^(n+1)-1) + 1.

1, 19, 127, 631, 2791, 11719, 48007, 194311, 781831, 3136519, 12564487, 50294791, 201252871, 805158919, 3220930567, 12884312071, 51538427911, 206156070919, 824629002247, 3298525446151, 13194120658951, 52776520384519, 211106157035527, 844424779137031

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).

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+12*x+8*x^2) / ( (x-1)*(2*x-1)*(4*x-1) ). (End)

Mathematica

CoefficientList[Series[-(1 + 12*x + 8*x^2)/((x-1)*(2*x-1)*(4*x-1)), {x, 0, 30}], x](* Vincenzo Librandi, Dec 03 2012 *)
LinearRecurrence[{7, -14, 8}, {1, 19, 127}, 30] (* Harvey P. Dale, Jan 15 2015 *)

Prog

(Magma) I:=[1, 19, 127]; [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 03 2012

Crossrefs

Cf. A169720-A169726, A000225.

Sequence in context: A142106 A078851 A202125 * A338300 A177459 A142649

Adjacent sequences: A169724 A169725 A169726 * A169728 A169729 A169730

Keyword

nonn,easy

Author

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

Extensions

G.f. adapted to the offset by Vincenzo Librandi, Dec 03 2012

Status

approved