A173197 a(0)=1, a(n)= 2+2^n/6+4*(-1)^n/3, n>0.

1, 1, 4, 2, 6, 6, 14, 22, 46, 86, 174, 342, 686, 1366, 2734, 5462, 10926, 21846, 43694, 87382, 174766, 349526, 699054, 1398102, 2796206, 5592406, 11184814, 22369622, 44739246, 89478486, 178956974, 357913942, 715827886, 1431655766, 2863311534, 5726623062, 11453246126, 22906492246, 45812984494, 91625968982, 183251937966, 366503875926, 733007751854

Offset: 0

Author

Paul Curtz, Feb 12 2010

Keywords

• nonn
• easy

Comments

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,...).

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

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

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

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (2,1,-2).

Formula

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

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

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

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

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