A168486 Numbers that are congruent to {2, 5} mod 11.

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

Offset

1,1

Links

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).

Formula

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

Mathematica

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 *)

Prog

(PARI) a(n) = (22*n - 5*(-1)^n - 19)/4 \\ David Lovler, Jul 16 2022

Crossrefs

Sequence in context: A049476 A216889 A334494 * A038914 A019419 A175256

Adjacent sequences: A168483 A168484 A168485 * A168487 A168488 A168489

Keyword

nonn,easy

Author

Vincenzo Librandi, Nov 27 2009

Extensions

Leading 2 added by R. J. Mathar, Jul 07 2015

Status

approved