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%I #42 Sep 03 2022 08:50:11
%S 4,6,12,14,20,22,28,30,36,38,44,46,52,54,60,62,68,70,76,78,84,86,92,
%T 94,100,102,108,110,116,118,124,126,132,134,140,142,148,150,156,158,
%U 164,166,172,174,180,182,188,190,196,198,204,206,212,214,220,222,228
%N Numbers that are congruent to {4, 6} mod 8.
%C In groups of four, add the odd and even numbers (4=1+3, 6=2+4; 12=5+7, 14=6+8; etc.). - _George E. Antoniou_, Dec 12 2001
%C The first 250 terms (4 through 998) are the 250 non-occurring Fibonacci number residues modulo 1000; i.e., if leading zeros are supplied as necessary for the terms having fewer than three digits, these are the 250 sets of three digits that never appear as the last three digits of a Fibonacci number. - _Jon E. Schoenfield_, Jul 05 2010
%H David Lovler, <a href="/A047406/b047406.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F a(n) = A042964(n)*2.
%F a(n) = (4*n - 1 - (-1)^n). - _Jon E. Schoenfield_, Jul 05 2010
%F a(n) = 8*n - a(n-1) - 6 (with a(1)=4). - _Vincenzo Librandi_, Aug 05 2010
%F G.f.: 2*x*(2+x+x^2) / ( (1+x)*(x-1)^2 ). - _R. J. Mathar_, Oct 08 2011
%F From _Wesley Ivan Hurt_, May 18 2013: (Start)
%F a(n) = (8 * ceiling(n/2) - 4) * (n mod 2) + (8 * ceiling(n/2) - 2) * (n+1 mod 2).
%F a(n) = 8 * ceiling(n/2) - 3 + (-1)^n. (End)
%F Sum_{n>=1} (-1)^(n+1)/a(n) = Pi/16 - log(2)/8. - _Amiram Eldar_, Dec 19 2021
%F E.g.f.: 2*(1 + 2*x*exp(x) - cosh(x)). - _David Lovler_, Sep 02 2022
%e a(2) = 8*2 - 4 - 6 = 6;
%e a(3) = 8*3 - 6 - 6 = 12;
%e a(4) = 8*4 - 12 - 6 = 14.
%t Select[Range[230], MemberQ[{4, 6}, Mod[#, 8]] &] (* _Amiram Eldar_, Dec 19 2021 *)
%o (PARI) a(n)=4*n-1-(-1)^n \\ _Charles R Greathouse IV_, May 20 2013
%Y Union of A017113 and A017137.
%Y Cf. A042964.
%K nonn,easy
%O 1,1
%A _N. J. A. Sloane_
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