A143988 Numbers congruent to {5, 13} mod 18.

5, 13, 23, 31, 41, 49, 59, 67, 77, 85, 95, 103, 113, 121, 131, 139, 149, 157, 167, 175, 185, 193, 203, 211, 221, 229, 239, 247, 257, 265, 275, 283, 293, 301, 311, 319, 329, 337, 347, 355, 365, 373, 383, 391, 401, 409, 419, 427, 437, 445, 455, 463, 473, 481

Offset

1,1

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Formula

a(n) = 18*(n-1) - a(n-1) for n > 1 and a(1)=5. - Vincenzo Librandi, Nov 25 2010

From Colin Barker, Oct 25 2019: (Start)

G.f.: x*(5 + 8*x + 5*x^2) / ((1 - x)^2*(1 + x)).

a(n) = a(n-1) + a(n-2) - a(n-3) for n>3.

a(n) = ((-1)^(1+n) + 18*n - 9) / 2. (End)

E.g.f.: 5 + ((18*x - 9)*exp(x) - exp(-x))/2. - David Lovler, Sep 08 2022

Sum_{n>=1} (-1)^(n+1)/a(n) = tan(2*Pi/9)*Pi/18. - Amiram Eldar, Feb 27 2023

Mathematica

Select[Range@ 500, MemberQ[{5, 13}, Mod[#, 18]] &] (* Michael De Vlieger, Nov 23 2018 *)

Prog

(GAP) Filtered([1..500], k->k mod 18 = 5 or k mod 18 = 13); # Muniru A Asiru, Nov 24 2018
(PARI) Vec(x*(5 + 8*x + 5*x^2) / ((1 - x)^2*(1 + x)) + O(x^60)) \\ Colin Barker, Oct 25 2019

Crossrefs

Sequence in context: A155142 A155552 A219546 * A129806 A125830 A049882

Adjacent sequences: A143985 A143986 A143987 * A143989 A143990 A143991

Keyword

nonn,easy

Author

Giovanni Teofilatto, Sep 07 2008

Extensions

Corrected (213 replaced with 211, 231 with 229, 249 with 247, 265 with 267 etc.) by R. J. Mathar, Apr 22 2010

Status

approved