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A169727
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a(n) = 3*(2^(n+1)-2)*(2^(n+1)-1) + 1.
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8
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1, 19, 127, 631, 2791, 11719, 48007, 194311, 781831, 3136519, 12564487, 50294791, 201252871, 805158919, 3220930567, 12884312071, 51538427911, 206156070919, 824629002247, 3298525446151, 13194120658951, 52776520384519, 211106157035527, 844424779137031
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OFFSET
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0,2
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COMMENTS
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A subsequence of the centered hexagonal numbers A003215.
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LINKS
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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).
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FORMULA
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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)
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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Cf. A169720-A169726, A000225.
Sequence in context: A142106 A078851 A202125 * A338300 A177459 A142649
Adjacent sequences: A169724 A169725 A169726 * A169728 A169729 A169730
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KEYWORD
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nonn,easy
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AUTHOR
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Alice V. Kleeva (alice27353(AT)gmail.com), Jan 19 2010
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EXTENSIONS
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G.f. adapted to the offset by Vincenzo Librandi, Dec 03 2012
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STATUS
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approved
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