login
A169727
a(n) = 3*(2^(n+1)-2)*(2^(n+1)-1) + 1.
8
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
Alice V. Kleeva, Grid for this sequence
Robert Munafo, Sequence A169720, and two others by Alice V. Kleeva [Cached copy, in pdf format, included with permission]
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
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