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A161734 a(n) = ((2+sqrt(2))*(5+sqrt(2))^n+(2-sqrt(2))*(5-sqrt(2))^n)/4. 3
1, 6, 37, 232, 1469, 9354, 59753, 382388, 2449561, 15700686, 100666957, 645553792, 4140197909, 26554241874, 170317866833, 1092431105228, 7007000115121, 44944085730966, 288279854661877, 1849084574806552, 11860409090842349, 76075145687872794 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Fifth binomial transform of A016116. Fourth binomial transform of the sequence of the absolute values of A077985. Third binomial transform of A007052. Second binomial transform of A086351. - R. J. Mathar, Jun 18 2009
LINKS
FORMULA
a(n) = 10*a(n-1) - 23*a(n-2). - R. J. Mathar, Jun 18 2009
G.f.: (1-4*x)/(1-10*x+23*x^2). - R. J. Mathar, Jun 18 2009
E.g.f.: exp(5*x)*(2*cosh(sqrt(2)*x) + sqrt(2)*sinh(sqrt(2)*x))/2. - G. C. Greubel, Apr 03 2018
MATHEMATICA
CoefficientList[Series[(1-4*z)/(23*z^2-10*z+1), {z, 0, 200}], z] (* Vladimir Joseph Stephan Orlovsky, Jun 12 2011 *)
LinearRecurrence[{10, -23}, {1, 6}, 50] (* G. C. Greubel, Apr 03 2018 *)
PROG
(PARI) F=nfinit(x^2-2); for(n=0, 20, print1(nfeltdiv(F, ((2+x)*(5+x)^n+(2-x)*(5-x)^n), 4)[1], ", ")) \\ Klaus Brockhaus, Jun 19 2009
(Magma) [Floor(((2+Sqrt(2))*(5+Sqrt(2))^n+(2-Sqrt(2))*(5-Sqrt(2))^n)/4): n in [0..30]]; // Vincenzo Librandi, Aug 18 2011
CROSSREFS
Sequence in context: A018904 A192807 A076026 * A081570 A122898 A317629
KEYWORD
nonn,easy
AUTHOR
Al Hakanson (hawkuu(AT)gmail.com), Jun 17 2009
EXTENSIONS
Extended by R. J. Mathar and Klaus Brockhaus, Jun 18 2009
Edited by Klaus Brockhaus, Jul 05 2009
STATUS
approved

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Last modified March 28 15:38 EDT 2024. Contains 371254 sequences. (Running on oeis4.)