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A321212 Numbers that are congruent to {2, 3} mod 16.

%I A321212 #78 Aug 20 2022 08:59:31
%S A321212 2,3,18,19,34,35,50,51,66,67,82,83,98,99,114,115,130,131,146,147,162,
%T A321212 163,178,179,194,195,210,211,226,227,242,243,258,259,274,275,290,291,
%U A321212 306,307,322,323,338,339,354,355,370,371,386,387,402,403,418,419,434,435,450,451,466,467,482,483,498,499
%N A321212 Numbers that are congruent to {2, 3} mod 16.
%H A321212 David Lovler, <a href="/A321212/b321212.txt">Table of n, a(n) for n = 1..10000</a>
%H A321212 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F A321212 a(n) = A151977(n) + 2.
%F A321212 G.f.: x*(2 + x + 13*x^2)/((-1 + x)^2*(1 + x)). - _Stefano Spezia_, Nov 01 2018
%F A321212 a(n) = a(n-1) + a(n-2) - a(n-3) for n > 3. - _Chai Wah Wu_, Nov 29 2018
%F A321212 From _Franck Maminirina Ramaharo_, Nov 30 2018: (Start)
%F A321212 a(n) = (16*n - 7*(-1)^n - 19)/2.
%F A321212 E.g.f.: (-7 + 26*exp(x) - 19*exp(2*x) + 16*x*exp(2*x))/(2*exp(x)). (End)
%F A321212 E.g.f.: 13 + ((16*x -19)*exp(x) - 7*exp(-x))/2. - _David Lovler_, Aug 20 2022
%F A321212 a(n) = a(n-2) + 16. - _David A. Corneth_, Nov 30 2018
%t A321212 Flatten@ Array[16 # + {2, 3} &, 31, 0] (* _Michael De Vlieger_, Oct 31 2018 *)
%t A321212 Select[Range[1, 500], MemberQ[{2,3}, Mod[#, 16]] &] (* _Vincenzo Librandi_, Nov 30 2018 *)
%o A321212 (Magma) [n: n in [1..500] | n mod 16 in [2, 3]]; // _Vincenzo Librandi_, Nov 30 2018
%o A321212 (PARI) a(n) = (16*n - 7*(-1)^n - 19)/2 \\ _David Lovler_, Aug 20 2022
%Y A321212 Cf. A047608, A151977.
%Y A321212 A091968 is a subsequence.
%K A321212 nonn,easy
%O A321212 1,1
%A A321212 _Yuen Biu_, Oct 31 2018