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A168486
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Numbers that are congruent to {2, 5} mod 11.
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1
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2, 5, 13, 16, 24, 27, 35, 38, 46, 49, 57, 60, 68, 71, 79, 82, 90, 93, 101, 104, 112, 115, 123, 126, 134, 137, 145, 148, 156, 159, 167, 170, 178, 181, 189, 192, 200, 203, 211, 214, 222, 225, 233, 236, 244, 247, 255, 258, 266, 269, 277, 280, 288, 291, 299, 302, 310
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OFFSET
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1,1
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LINKS
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David Lovler, Table of n, a(n) for n = 1..10000 (first 1000 terms from Vincenzo Librandi)
Index entries for linear recurrences with constant coefficients, signature (1,1,-1).
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FORMULA
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a(n) = 11*n - a(n-1) - 4 with n>1, a(1)=2.
From R. J. Mathar, Mar 21 2010, Jul 07 2015: (Start)
a(n) = (22*n - 5*(-1)^n - 19)/4.
a(n) = a(n-1) + a(n-2) - a(n-3).
G.f.: x*(2 + 3*x + 6*x^2)/ ((1+x) * (x-1)^2). (End)
E.g.f.: (1/2)*(12 + (11*x - 12)*cosh(x) + (11*x - 7)*sinh(x)). - G. C. Greubel, Jul 23 2016
E.g.f.: (12 + (11*x -12)*exp(x) + 5*sinh(x))/2. - David Lovler, Jul 16 2022
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MATHEMATICA
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Select[Range[310], MemberQ[{2, 5}, Mod[#, 11]]&] (* Ray Chandler, Jul 07 2015 *)
LinearRecurrence[{1, 1, -1}, {2, 5, 13}, 57] (* Ray Chandler, Jul 07 2015 *)
Rest[CoefficientList[Series[x*(2+3*x+6*x^2)/((1+x)*(x-1)^2), {x, 0, 57}], x] ] (* Ray Chandler, Jul 07 2015 *)
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PROG
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(PARI) a(n) = (22*n - 5*(-1)^n - 19)/4 \\ David Lovler, Jul 16 2022
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CROSSREFS
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Sequence in context: A049476 A216889 A334494 * A038914 A019419 A175256
Adjacent sequences: A168483 A168484 A168485 * A168487 A168488 A168489
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KEYWORD
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nonn,easy
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AUTHOR
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Vincenzo Librandi, Nov 27 2009
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EXTENSIONS
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Leading 2 added by R. J. Mathar, Jul 07 2015
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STATUS
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approved
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