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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
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OFFSET
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0,2
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COMMENTS
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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
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LINKS
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FORMULA
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E.g.f.: exp(5*x)*(2*cosh(sqrt(2)*x) + sqrt(2)*sinh(sqrt(2)*x))/2. - G. C. Greubel, Apr 03 2018
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MATHEMATICA
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LinearRecurrence[{10, -23}, {1, 6}, 50] (* G. C. Greubel, Apr 03 2018 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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Al Hakanson (hawkuu(AT)gmail.com), Jun 17 2009
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EXTENSIONS
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STATUS
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approved
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