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A124610 a(n) = 5*a(n-1) + 2*a(n-2), n>1; a(0) = a(1) = 1. 2
1, 1, 7, 37, 199, 1069, 5743, 30853, 165751, 890461, 4783807, 25699957, 138067399, 741736909, 3984819343, 21407570533, 115007491351, 617852597821, 3319277971807, 17832095054677, 95799031216999, 514659346194349 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Top left element of powers of the matrix [1,2;3,4].

LINKS

Table of n, a(n) for n=0..21.

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

FORMULA

a(n)/a(n-1) tends to (sqrt(33) + 5)/2 = 5.37228132... - Gary W. Adamson, Mar 03 2008

a(n)=-(1/22)*sqrt(33)*[5/2+(1/2)*sqrt(33)]^n+(1/2)*[5/2-(1/2)*sqrt(33)]^n+(1/22)*[5/2-(1/2) *sqrt(33)]^n*sqrt(33)+(1/2)*[5/2+(1/2)*sqrt(33)]^n, with n>=0 - Paolo P. Lava, Jul 07 2008

EXAMPLE

a(5) = 1069 because [1,2;3,4]^5 = [1069,1558;2337,3406]

MATHEMATICA

Table[MatrixPower[{{1, 2}, {3, 4}}, n][[1]][[1]], {n, 0, 30}]

Transpose[NestList[Flatten[{Rest[#], ListCorrelate[{2, 5}, #]}]&, {1, 1}, 40]][[1]]  (* Harvey P. Dale, Mar 23 2011 *)

LinearRecurrence[{5, 2}, {1, 1}, 30] (* Harvey P. Dale, Jan 01 2014 *)

CROSSREFS

Cf. A100638.

Sequence in context: A287808 A117130 A002807 * A002683 A126475 A274674

Adjacent sequences:  A124607 A124608 A124609 * A124611 A124612 A124613

KEYWORD

easy,nonn

AUTHOR

Fredrik Johansson, Dec 20 2006

EXTENSIONS

Recurrence from Gary W. Adamson, Mar 03 2008

STATUS

approved

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Last modified November 19 01:27 EST 2017. Contains 294912 sequences.