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A166154
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a(n) = 7*n*(n+1)/2 - 5.
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1
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2, 16, 37, 65, 100, 142, 191, 247, 310, 380, 457, 541, 632, 730, 835, 947, 1066, 1192, 1325, 1465, 1612, 1766, 1927, 2095, 2270, 2452, 2641, 2837, 3040, 3250, 3467, 3691, 3922, 4160, 4405, 4657, 4916, 5182, 5455, 5735, 6022, 6316, 6617, 6925, 7240, 7562
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OFFSET
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1,1
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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 (3,-3,1).
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FORMULA
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a(n) = A166146(n)+1.
a(n) = a(n-1)+7*n = 3*a(n-1) -3*a(n-2) +a(n-3).
G.f.: x*(-2-10*x+5*x^2)/(x-1)^3.
E.g.f.: (7/2)*((x^2 + 2*x - 5)*exp(x) + 5). - G. C. Greubel, May 01 2016
Sum_{n>=1} 1/a(n) = 1/5 + (2*Pi/sqrt(329))*tan(sqrt(47/7)*Pi/2). - Amiram Eldar, Feb 20 2023
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MATHEMATICA
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Table[7 n (n + 1)/2 - 5, {n, 100}] (* or *) CoefficientList[Series[(- 2 - 10 x + 5 x^2) / (x - 1)^3, {x, 0, 50}], x] (* Vincenzo Librandi, Sep 13 2013 *)
LinearRecurrence[{3, -3, 1}, {2, 16, 37}, 50] (* G. C. Greubel, May 01 2016 *)
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PROG
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(Magma) [7*n*(n+1)/2-5: n in [1..50]]; // Vincenzo Librandi, Sep 13 2013
(PARI) a(n)=7*n*(n+1)/2-5 \\ Charles R Greathouse IV, May 02 2016
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CROSSREFS
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Cf. A166146.
Sequence in context: A019064 A123135 A327542 * A034507 A211620 A023638
Adjacent sequences: A166151 A166152 A166153 * A166155 A166156 A166157
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KEYWORD
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nonn,easy
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AUTHOR
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Vincenzo Librandi, Oct 08 2009
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EXTENSIONS
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Definition replaced by polynomial, A-number corrected, formulas added by R. J. Mathar, Oct 12 2009
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STATUS
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approved
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