A161734 a(n) = ((2+sqrt(2))*(5+sqrt(2))^n+(2-sqrt(2))*(5-sqrt(2))^n)/4.

1, 6, 37, 232, 1469, 9354, 59753, 382388, 2449561, 15700686, 100666957, 645553792, 4140197909, 26554241874, 170317866833, 1092431105228, 7007000115121, 44944085730966, 288279854661877, 1849084574806552, 11860409090842349, 76075145687872794

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

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (10,-23).

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

Cf. A016116, A077985, A000129, A007052, A086351.

Sequence in context: A018904 A192807 A076026 * A081570 A122898 A317629

Adjacent sequences: A161731 A161732 A161733 * A161735 A161736 A161737

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