A176968 Expansion of x*( 1+2*x-x^2-6*x^3 ) / ( 1-9*x^2+12*x^4 ).

1, 2, 8, 12, 60, 84, 444, 612, 3276, 4500, 24156, 33156, 178092, 244404, 1312956, 1801764, 9679500, 13283028, 71360028, 97926084, 526086252, 721938420, 3878455932, 5322332772, 28593068364, 39237733908, 210796144092

Offset

1,2

Comments

The ratio a(n+1)/a(n) alternates between 5.3722813232690143299 and 1.3722813232690143299.

Links

Table of n, a(n) for n=1..27.

Index entries for linear recurrences with constant coefficients, signature (0,9,0,-12).

Formula

Given the auxiliary b(0)=b(1)=1 and b(n) = b(n-1)/2 + b(n-2) *sqrt(5-(-1)^n*4) /2, a(n) =2^(n-1)*b(n).

a(n) = a(n-1)+6*a(n-2) if n is odd. a(n) = a(n-1)+2*a(n-2) if n is even. - R. J. Mathar, Jun 18 2014

Mathematica

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

Crossrefs

Sequence in context: A280092 A083546 A013190 * A308935 A126192 A272720

Adjacent sequences: A176965 A176966 A176967 * A176969 A176970 A176971

Keyword

nonn,easy

Author

Roger L. Bagula, Apr 29 2010

Status

approved