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A140184 a(n) = 2*a(n-1) + 16*a(n-2) + 16*a(n-3). 0
1, 14, 60, 360, 1904, 10528, 57280, 313472, 1711872, 9355776, 51117056, 279316480, 1526198272, 8339333120, 45566902272, 248982306816, 1360464379904, 7433716105216, 40618579197952, 221944046157824, 1212724817166336, 6626451640025088, 36207605093236736 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n)/a(n-1) tends to (2*sqrt(3) + 2) = an eigenvalue of matrix X and a root to the characteristic polynomial x^3 - 2x^2 - 16x - 16.

LINKS

Table of n, a(n) for n=1..23.

Index entries for linear recurrences with constant coefficients, signature (2, 16, 16).

FORMULA

a(n) - 2*a(n-1) + 16*a(n-2) + 16*a(n-3); for n>3, given a(1) = 1, a(2) = 14, a(3) = 60. Term (1,1) of X^n, where X = the 3x3 matrix [1,2,3; 2,0,2; 3,2,1].

a(n) = (2/3)*[2+2*sqrt(3)]^n*sqrt(3)+[2+2*sqrt(3)]^n+[2-2*sqrt(3)]^n-(-2)^n-(2/3)*sqrt(3) *[2-2*sqrt(3)]^n, with n>= 0 - Paolo P. Lava, Jun 06 2008

G.f.: -x*(1+12*x+16*x^2) / ( (2*x+1)*(8*x^2+4*x-1) ) [From Harvey P. Dale, May 03 2011]

a(n) = ( A180222(n+2) +(-2)^n)/2. - R. J. Mathar, Oct 08 2016

EXAMPLE

a(5) = 1904 = 2*a(4) + 16*a(3) + 16*a(2) = 2*360 + 16*60 + 16*14.

a(4) = 360 since term (1,1) of X^4 = 360.

MATHEMATICA

LinearRecurrence[{2, 16, 16}, {1, 14, 60}, 40] (* or *) CoefficientList[Series[(-1-12 x-16 x^2)/(-1+2 x+16 x^2+16 x^3), {x, 0, 40}], x] (* Harvey P. Dale, May 03 2011 *)

CROSSREFS

Sequence in context: A063492 A051799 A164540 * A264854 A189948 A252255

Adjacent sequences:  A140181 A140182 A140183 * A140185 A140186 A140187

KEYWORD

nonn,easy

AUTHOR

Gary W. Adamson, May 11 2008

STATUS

approved

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Last modified December 14 12:04 EST 2019. Contains 329979 sequences. (Running on oeis4.)