%I #29 Nov 23 2024 05:41:42
%S 4,6,14,16,24,26,34,36,44,46,54,56,64,66,74,76,84,86,94,96,104,106,
%T 114,116,124,126,134,136,144,146,154,156,164,166,174,176,184,186,194,
%U 196,204,206,214,216,224,226,234,236,244,246,254,256,264,266,274,276,284
%N Numbers that are congruent to {4, 6} mod 10.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F a(n) = 2 * A047221(n) = 5*n-5/2-3*(-1)^n/2.
%F a(n) = 10*n-a(n-1)-10 (with a(1)=4). - _Vincenzo Librandi_, Nov 16 2010
%F G.f.: 2*x*(2+x+2*x^2) / ( (1+x)*(x-1)^2 ). - _R. J. Mathar_, Oct 08 2011
%F Sum_{n>=1} (-1)^(n+1)/a(n) = sqrt(1-2/sqrt(5))*Pi/10. - _Amiram Eldar_, Dec 28 2021
%F From _Amiram Eldar_, Nov 23 2024: (Start)
%F Product_{n>=1} (1 - (-1)^n/a(n)) = cosec(2*Pi/5) (A179290).
%F Product_{n>=1} (1 + (-1)^n/a(n)) = cosec(Pi/5)/2 (A300074). (End)
%t #+{4,6}&/@(10Range[0,50])//Flatten (* or *) LinearRecurrence[{1,1,-1},{4,6,14},100] (* _Harvey P. Dale_, Jun 05 2017 *)
%Y Cf. A047221, A090298, A179290, A300074.
%K nonn
%O 1,1
%A _Giovanni Teofilatto_, Feb 07 2004
%E Edited and extended by _Ray Chandler_, Feb 10 2004