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%I A340627 #47 May 07 2021 09:39:25
%S A340627 3,8,14,30,58,118,234,470,938,1878,3754,7510,15018,30038,60074,120150,
%T A340627 240298,480598,961194,1922390,3844778,7689558,15379114,30758230,
%U A340627 61516458,123032918,246065834,492131670,984263338,1968526678,3937053354,7874106710,15748213418,31496426838
%N A340627 a(n) = (11*2^n - 2*(-1)^n)/3 for n >= 0.
%C A340627 Based on A112387.
%C A340627 Prepended with 0, 1, its difference table is
%C A340627 0,  1,  1,  2,  1,   4,  3,   8, ... = mix A001045(n), 2^n.
%C A340627 1,  0,  1, -1,  3,  -1,  5,  -3, ... = mix A001045(n+1), -A001045(n).
%C A340627 -1, 1, -2,  4, -4,   6, -8,  14, ... = mix -2^n, A084214(n+1).
%C A340627 2, -3,  6, -8, 10, -14, 22, -30, ... = mix 2*A001045(n+2), -a(n).
%H A340627 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (1,2).
%F A340627 a(n) = 2^(n+2) - A078008(n), n>=0.
%F A340627 a(n) = (A062510(n) = 3*A001045(n)) + A001045(n+3), n>=0.
%F A340627 a(0)=3, a(2*n+1) = 2*a(2*n) + 2, a(2*n+2) = 2*a(2*n+1) - 2, n>=0.
%F A340627 a(n) = 4*A052997(n-1) + 2, n>=2. - _Hugo Pfoertner_, Apr 25 2021
%F A340627 a(n+1) = 11*2^n - a(n) for n>=0.
%F A340627 a(n+3) = 33*2^n - a(n) for n>=0.
%F A340627 a(n+5) = 121*2^n - a(n) for n>=0.
%F A340627 etc.
%F A340627 a(n+2) = a(n) + 11*2^n for n>=0.
%F A340627 a(n+4) = a(n) + 55*2^n for n>=0.
%F A340627 a(n+6) = a(n) + 231*2^n for n>=0.
%F A340627 etc.
%F A340627 G.f.: (3 + 5*x)/(1 - x - 2*x^2). - _Stefano Spezia_, Apr 26 2021
%F A340627 E.g.f: (11*exp(2*x) - 2*exp(-x))/3. - _Jianing Song_, Apr 26 2021
%t A340627 LinearRecurrence[{1, 2}, {3, 8}, 35] (* _Amiram Eldar_, Apr 25 2021 *)
%o A340627 (PARI) a(n) = (11*2^n - 2*(-1)^n)/3 \\ _Felix Fröhlich_, Apr 25 2021
%Y A340627 Cf. A000079, A001045, A062510, A078008, A112387.
%Y A340627 Cf. also A052997.
%K A340627 nonn,easy
%O A340627 0,1
%A A340627 _Paul Curtz_, Apr 25 2021
%E A340627 More terms from _Michel Marcus_, Apr 25 2021
%E A340627 New name from _Jianing Song_, Apr 25 2021

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