A176961 a(n) = (3*2^(n+1) - 8 - (-2)^n)/6.

1, 2, 8, 12, 36, 52, 148, 212, 596, 852, 2388, 3412, 9556, 13652, 38228, 54612, 152916, 218452, 611668, 873812, 2446676, 3495252, 9786708, 13981012, 39146836, 55924052, 156587348, 223696212, 626349396, 894784852

Offset: 1

Author

Roger L. Bagula, Apr 29 2010

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (1,4,-4).

Programs

Magma

[(3*2^(n+1)-8-(-2)^n)/6:n in [1..40]]; // Vincenzo Librandi, Sep 15 2011

Mathematica

a[1] := 1;
a[n_] := a[n] = a[n - 1]/2 + Sqrt[(5 + 4*(-1)^(n - 1))]/2:
Table[2^(n - 1)*a[n], {n, 1, 30}]

PARI

a(n)=(3<<(n+1)-(-2)^n)\/6-1 \\ Charles R Greathouse IV, Sep 14 2011

Formula

a(n) - a(n-1) = A081631(n-2).

a(n) = a(n-1) + 4*a(n-2) - 4*a(n-3).

G.f.: x*(1 + x + 2*x^2) / ((x-1)*(2*x+1)*(2*x-1)). - R. J. Mathar, Apr 30 2010

a(n) = 2^n - A084247(n-1). - Bruno Berselli, Sep 15 2011