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A161734
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a(n) = ((2+sqrt(2))*(5+sqrt(2))^n+(2-sqrt(2))*(5-sqrt(2))^n)/4.
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3
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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; internal format)
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OFFSET
| 0,2
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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. [From R. J. Mathar, Jun 18 2009]
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..1000
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FORMULA
| a(n) = 10*a(n-1)-23*a(n-2). G.f.: (1-4*x)/(1-10*x+23*x^2). [From R. J. Mathar, Jun 18 2009]
G.f.: (1-4*x)/(1-10*x+23*x^2). [From Klaus Brockhaus, Jun 19 2009]
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MATHEMATICA
| CoefficientList[Series[(1 - 4 z)/(23 z^2 - 10 z + 1), {z, 0, 200}], z] (* From Vladimir Joseph Stephan Orlovsky, Jun 12 2011 *)
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PROG
| (PARI) {default(debug, 0); F=nfinit(x^2-2); for(n=0, 20, print1(nfeltdiv(F, ((2+x)*(5+x)^n+(2-x)*(5-x)^n), 4)[1], ", "))} [From 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
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CROSSREFS
| Cf. A016116, A077985, A000129, A007052, A086351.
Sequence in context: A018904 A192807 A076026 * A081570 A122898 A081912
Adjacent sequences: A161731 A161732 A161733 * A161735 A161736 A161737
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KEYWORD
| nonn
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AUTHOR
| Al Hakanson (hawkuu(AT)gmail.com), Jun 17 2009
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EXTENSIONS
| Extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl) and Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jun 18 2009
Edited by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jul 05 2009
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