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

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).

Crossrefs

Cf. A169720-A169726, A000225.

Programs

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

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 *)

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)

Extensions

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