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A168409
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a(n) = 8 + 9*floor((n-1)/2).
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1
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8, 8, 17, 17, 26, 26, 35, 35, 44, 44, 53, 53, 62, 62, 71, 71, 80, 80, 89, 89, 98, 98, 107, 107, 116, 116, 125, 125, 134, 134, 143, 143, 152, 152, 161, 161, 170, 170, 179, 179, 188, 188, 197, 197, 206, 206, 215, 215, 224, 224, 233, 233, 242, 242, 251, 251, 260
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OFFSET
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1,1
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COMMENTS
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Old definition: "a(n)=9*n-a(n-1)-2 (with a(1)=8)".
The sequences generated by the recursive relation b(n) = h*n-b(n-1)+k, with b(1)=c and h, k, c prefixed integers, satisfy the formula b(n) = c + h*floor((n-1)/2) when 2*h+k = 2*c. - Bruno Berselli, Sep 18 2013
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,1,-1).
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FORMULA
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a(n) = 9*n - a(n-1) - 2, with n>1, a(1)=8.
a(n) = (5 - 9*(-1)^n + 18*n)/4. - Paolo P. Lava, Nov 27 2009
a(1)=8, a(2)=8, a(3)=17; for n>1, a(n) = a(n-1) +a(n-2) -a(n-3). - Harvey P. Dale, Aug 18 2013
G.f.: x*(8 + x^2)/((1+x)*(x-1)^2). - Vincenzo Librandi, Sep 18 2013
E.g.f.: (1/4)*(-9 + 4*exp(x) + (5 + 18*x)*exp(2*x))*exp(-x). - G. C. Greubel, Jul 21 2016
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MATHEMATICA
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RecurrenceTable[{a[1]==8, a[n]==9n-a[n-1]-2}, a, {n, 60}] (* or *) LinearRecurrence[{1, 1, -1}, {8, 8, 17}, 80] (* or *) With[{c = LinearRecurrence[{2, -1}, {8, 17}, 30]}, Riffle[c, c]] (* Harvey P. Dale, Aug 18 2013 *)
CoefficientList[Series[(8 + x^2)/((1 + x) (x - 1)^2), {x, 0, 70}], x] (* Vincenzo Librandi, Sep 18 2013 *)
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PROG
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(MAGMA) [8+9*Floor((n-1)/2): n in [1..70]]; // Vincenzo Librandi, Sep 18 2013
(PARI) a(n)=(n-1)\2*9 + 8 \\ Charles R Greathouse IV, Jul 21 2016
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CROSSREFS
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Cf. A017257.
Sequence in context: A022091 A171188 A145909 * A135405 A006784 A214830
Adjacent sequences: A168406 A168407 A168408 * A168410 A168411 A168412
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KEYWORD
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nonn,easy,less
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AUTHOR
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Vincenzo Librandi, Nov 25 2009
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EXTENSIONS
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New definition by Vincenzo Librandi, Sep 18 2013
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STATUS
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approved
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