A080882 a(n)*a(n+3) - a(n+1)*a(n+2) = 2^n, given a(0)=1, a(1)=3, a(2)=7.

1, 3, 7, 22, 52, 164, 388, 1224, 2896, 9136, 21616, 68192, 161344, 508992, 1204288, 3799168, 8988928, 28357376, 67094272, 211662336, 500798464, 1579869184, 3738010624, 11792304128, 27900891136, 88018956288, 208255086592

Offset

0,2

Links

Table of n, a(n) for n=0..26.

Formula

G.f.: (-2*x^3 - x^2 + 3*x + 1)/(4*x^4 - 8*x^2 + 1).

a(n + 4) = 8*a(n + 2) - 4*a(n). - Richard Choulet, Dec 06 2008

a(n) = (7/24*3^(1/2) + 1/2)*((1 + sqrt(3)))^n + ( - 7/24*3^(1/2) + 1/2)*((1 - sqrt(3)))^n + ( - 1/24*3^(1/2))*( - (1 + sqrt(3)))^n + (1/24*3^(1/2))*( - ((1 - sqrt(3))))^n. - Richard Choulet, Dec 06 2008

Maple

a:= n-> (Matrix([[22, 7, 3, 1]]). Matrix(4, (i, j)-> if (i=j-1) then 1 elif j=1 then [0, 8, 0, -4][i] else 0 fi)^(n))[1, 4]: seq(a(n), n=0..26); # Alois P. Heinz, Aug 23 2008

Mathematica

a[0]=1; a[1]=3; a[2]=7; a[3]=22; a[n_] := a[n] = 8*a[n-2] - 4*a[n-4]; Table[a[n], {n, 0, 26}] (* Jean-François Alcover, Jun 15 2015, after Richard Choulet *)

Crossrefs

Cf. A080876, A080877, A080878, A080879, A080880, A080881.

a(2n)=A080879(2n+1)=A080876(2n+4)/4, a(2n+1)=A080879(2n+2)/2=A080876(2n+5)/4.

Sequence in context: A174942 A128599 A182174 * A229807 A229900 A079120

Adjacent sequences: A080879 A080880 A080881 * A080883 A080884 A080885

Keyword

nonn

Author

Paul D. Hanna, Feb 22 2003

Status

approved