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 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 (list; graph; refs; listen; history; text; internal format)
 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 * A177459 A142649 A020867 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

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