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%I #47 Mar 30 2024 11:38:47
%S 3,6,11,14,19,22,27,30,35,38,43,46,51,54,59,62,67,70,75,78,83,86,91,
%T 94,99,102,107,110,115,118,123,126,131,134,139,142,147,150,155,158,
%U 163,166,171,174,179,182,187,190,195,198,203,206,211,214,219,222,227,230
%N Numbers that are congruent to {3, 6} mod 8.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F a(n) = 8*n - a(n-1) - 7, n > 1. - _Vincenzo Librandi_, Aug 05 2010
%F From _R. J. Mathar_, Dec 05 2011: (Start)
%F a(n) = 4*n - (3 + (-1)^n)/2.
%F G.f.: x*(3+3*x+2*x^2) / ( (1+x)*(x-1)^2 ). (End)
%F From _Franck Maminirina Ramaharo_, Aug 06 2018: (Start)
%F a(n) = a(n-1) + a(n-2) - a(n-3), n > 3.
%F a(n) = 4*n + (n mod 2) - 2.
%F a(n) = A047470(n) + 3.
%F a(2*n) = A017137(n-1).
%F a(2*n-1) = A017101(n-1).
%F E.g.f.: ((8*x - 3)*exp(x) - exp(-x) + 4)/2. (End)
%F Sum_{n>=1} (-1)^(n+1)/a(n) = sqrt(2)*Pi/16 + log(2)/8 - sqrt(2)*log(sqrt(2)+1)/8. - _Amiram Eldar_, Dec 18 2021
%p A047398:=n->4*n-(3+(-1)^n)/2: seq(A047398(n), n=1..100); # _Wesley Ivan Hurt_, Jan 30 2017
%t Flatten[# + {3, 6} & /@ (8 Range[0, 28])] (* _Arkadiusz Wesolowski_, Sep 25 2012 *)
%t LinearRecurrence[{1,1,-1},{3,6,11},60] (* _Harvey P. Dale_, Oct 26 2020 *)
%o (Maxima) makelist(4*n + mod(n, 2) - 2, n, 1, 100); /* _Franck Maminirina Ramaharo_, Aug 06 2018 */
%o (Python)
%o def A047398(n): return ((n<<2)|(n&1))-2 # _Chai Wah Wu_, Mar 30 2024
%Y Union of A017101 and A017137.
%Y Cf. A047461, A047452, A047470, A047524, A047535, A047615, A047617.
%K nonn,easy
%O 1,1
%A _N. J. A. Sloane_
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