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A041612 Numerators of continued fraction convergents to sqrt(325). 2
18, 649, 23382, 842401, 30349818, 1093435849, 39394040382, 1419278889601, 51133434066018, 1842222905266249, 66371158023650982, 2391203911756701601, 86149711981264908618, 3103780835237293411849, 111822259780523827735182, 4028705132934095091878401 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Tanya Khovanova, Recursive Sequences

Index entries for linear recurrences with constant coefficients, signature (36,1).

FORMULA

a(n)=36*a(n-1)+a(n-2), n>1 ; a(0)=18, a(1)=649 . G.f.: (18+x)/(1-36*x-x^2). [From Philippe Deléham, Nov 23 2008]

a(n)=9*{[18+5*sqrt(13)]^n+[18-5*sqrt(13)]^n}+(5/2)*sqrt(13)*{[18+5*sqrt(13)]^n-[18-5*sqrt(13)]^n}, with n>=0 [From Paolo P. Lava, Nov 28 2008]

MATHEMATICA

Numerator[Convergents[Sqrt[325], 30]] (* Vincenzo Librandi, Nov 04 2013 *)

CROSSREFS

Cf. A041613.

Sequence in context: A003298 A049869 A041615 * A046674 A073421 A159873

Adjacent sequences:  A041609 A041610 A041611 * A041613 A041614 A041615

KEYWORD

nonn,cofr,frac,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

Additional term from Colin Barker, Nov 09 2013

STATUS

approved

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Last modified July 22 12:46 EDT 2017. Contains 289669 sequences.