A173197 - OEIS

%I #15 Jun 13 2015 00:53:28

%S 1,1,4,2,6,6,14,22,46,86,174,342,686,1366,2734,5462,10926,21846,43694,

%T 87382,174766,349526,699054,1398102,2796206,5592406,11184814,22369622,

%U 44739246,89478486,178956974,357913942,715827886,1431655766,2863311534,5726623062,11453246126,22906492246,45812984494,91625968982,183251937966,366503875926,733007751854

%N a(0)=1, a(n)= 2+2^n/6+4*(-1)^n/3, n>0.

%C Linked to Jacobsthal numbers (expansion of tan(x), a.k.a. Zag numbers) A000182=1,2,16,272,...: a(n+1)-2a(n) = -(-1)^n*(A000182(n) mod 10) = (-1,2,-6,2,-6,2,-6,...).

%C Cf. A173114, related to Euler (or secant, or Zig) numbers, A000364. a(n+1)+A010684=A001045.

%C First differences: 0,3,-2,4,0,8,8,24,... = 0,A154879 (third differences of A001045).

%C Main diagonal: A003945; first upper diagonal: -A171449; second: 4*A011782.

%H Vincenzo Librandi, <a href="/A173197/b173197.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,-2).

%F a(n) = A093380(n+4), n>3.

%F a(n) = +2*a(n-1) +a(n-2) -2*a(n-3), n>3.

%F G.f.: 1-x*(-1-2*x+7*x^2)/((x-1)*(2*x-1)*(1+x)).

%F a(2n+2)+a(2n+3)=6*A047689.

%F a(2n)-a(2n-2) = 3,1,2,4,8,16,... = 3,A000079.

%K nonn,easy

%O 0,3

%A _Paul Curtz_, Feb 12 2010