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A199023
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(6*11^n - 1) / 5.
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6
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1, 13, 145, 1597, 17569, 193261, 2125873, 23384605, 257230657, 2829537229, 31124909521, 342374004733, 3766114052065, 41427254572717, 455699800299889, 5012697803298781, 55139675836286593, 606536434199152525
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OFFSET
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0,2
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COMMENTS
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Sum of n-th row of triangle of powers of 11: 1; 1 11 1; 1 11 121 11 1; 1 11 121 1331 121 11 1; ... - Philippe Deléham, Feb 23 2014
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..900
Index entries for linear recurrences with constant coefficients, signature (12,-11).
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FORMULA
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a(n) = 11*a(n-1)+2.
a(n) = 12*a(n-1)-11*a(n-2), n>1.
G.f.: (1 + x)/(1 - 12*x + 11*x^2). - Vincenzo Librandi, Jan 04 2013
a(n) = Sum_{k=0..n} A112468(n,k)*12^k. - Philippe Deléham, Feb 23 2014
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EXAMPLE
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a(0) = 1;
a(1) = 1 + 11 + 1 = 13;
a(2) = 1 + 11 + 121 + 11 + 1 = 145;
a(3) = 1 + 11 + 121 + 1331 + 121 + 11 + 1 = 1597; etc. - Philippe Deléham, Feb 23 2014
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MATHEMATICA
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CoefficientList[Series[(1 + x)/(1 - 12*x + 11*x^2), {x, 0, 30}], x] (* Vincenzo Librandi, Jan 04 2013 *)
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PROG
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(Magma) [(6*11^n-1)/5 : n in [0..20]]
(PARI) a(n)=(6*11^n-1)/5 \\ Charles R Greathouse IV, Oct 07 2015
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CROSSREFS
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Cf. A112468, A112739.
Sequence in context: A038492 A270579 A297223 * A152585 A014881 A048442
Adjacent sequences: A199020 A199021 A199022 * A199024 A199025 A199026
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KEYWORD
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nonn,easy
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AUTHOR
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Vincenzo Librandi, Nov 02 2011
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STATUS
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approved
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