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A135139 a(n) = 5*a(n-2) + 2*a(n-3). 2
1, 2, 4, 12, 24, 68, 144, 388, 856, 2228, 5056, 12852, 29736, 74372, 174384, 431332, 1020664, 2505428, 5965984, 14568468, 34840776, 84774308, 203340816, 493553092, 1186252696, 2874447092, 6918369664, 16744740852, 40340742504, 97560443588 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0, 5, 2).

FORMULA

From R. J. Mathar, Feb 15 2008: (Start)

O.g.f.: 4(x-2)/[7(x^2+2x-1) - 1/[7(1+2x)].

a(n) = [4*A078343(n+1)-(-2)^n]/7.

a(n) = A135138(n+2) + 2*A135138(n+1) - A135138(n). (End)

a(n) = (4/7)*[1+sqrt(2)]^n - (1/7)*sqrt(2)*[1-sqrt(2)]^n - (1/7)*(-2)^n + (4/7)*[1-sqrt(2)]^n + (1/7)*[1 +sqrt(2)]^n*sqrt(2), with n>=0. - Paolo P. Lava, Jun 09 2008

MATHEMATICA

a = {1, 2, 4}; Do[AppendTo[a, 5*a[[ -2]] + 2*a[[ -3]]], {40}]; a (* Stefan Steinerberger, Feb 15 2008 *)

LinearRecurrence[{0, 5, 2}, {1, 2, 4}, 30] (* Harvey P. Dale, May 25 2012 *)

CROSSREFS

Cf. A135138.

Sequence in context: A331392 A100538 A303794 * A161894 A062177 A129643

Adjacent sequences:  A135136 A135137 A135138 * A135140 A135141 A135142

KEYWORD

nonn

AUTHOR

Paul Curtz, Feb 13 2008

EXTENSIONS

More terms from R. J. Mathar and Stefan Steinerberger, Feb 15 2008

STATUS

approved

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Last modified September 21 07:28 EDT 2021. Contains 347596 sequences. (Running on oeis4.)