A047248 - OEIS

%I #26 Dec 17 2021 10:14:04

%S 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,

%T 30,32,33,34,35,36,38,39,40,41,42,44,45,46,47,48,50,51,52,53,54,56,57,

%U 58,59,60,62,63,64,65,66,68

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

%H G. C. Greubel, <a href="/A047248/b047248.txt">Table of n, a(n) for n = 1..5000</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,1,-1).

%F 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

%F 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

%t 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 *)

%t DeleteCases[Range[0,70],_?(Mod[#,6]==1&)] (* or *) Complement[ Range[ 0,70], Range[1,70,6]] (* _Harvey P. Dale_, Dec 30 2017 *)

%o (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

%Y Cf. A047252.

%K nonn

%O 1,2

%A _N. J. A. Sloane_