A047248 Numbers that are congruent to {0, 2, 3, 4, 5} (mod 6).

0, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 26, 27, 28, 29, 30, 32, 33, 34, 35, 36, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 50, 51, 52, 53, 54, 56, 57, 58, 59, 60, 62, 63, 64, 65, 66, 68

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..5000
• Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,1,-1).

Crossrefs

Cf. A047252.

Programs

Mathematica

Rest[CoefficientList[Series[x^2*(2 + x + x^2 + x^3 + x^4)/((x^4 + x^3 + x^2 + x + 1)*(x - 1)^2), {x, 0, 50}], x]] (* G. C. Greubel, Nov 02 2017 *)
DeleteCases[Range[0,70],?(Mod[#,6]==1&)] (* or *) Complement[ Range[ 0,70], Range[1,70,6]] (* _Harvey P. Dale, Dec 30 2017 *)

PARI

x='x+O('x^50); concat([0], Vec(x^2*(2+x+x^2+x^3+x^4)/((x^4 +x^3 +x^2 +x+1)*(x-1)^2))) \\ G. C. Greubel, Nov 02 2017

Formula

G.f.: x^2*(2+x+x^2+x^3+x^4) / ( (x^4+x^3+x^2+x+1)*(x-1)^2 ). - R. J. Mathar, Oct 08 2011

Sum_{n>=2} (-1)^n/a(n) = log(2+sqrt(3))/(2*sqrt(3)) + log(2)/6 - (9-4*sqrt(3))*Pi/36. - Amiram Eldar, Dec 17 2021