A161727 a(n) = ((2+sqrt(3))*(4+sqrt(3))^n-(2-sqrt(3))*(4-sqrt(3))^n)/sqrt(12).

1, 6, 35, 202, 1161, 6662, 38203, 219018, 1255505, 7196806, 41252883, 236464586, 1355429209, 7769394054, 44534572715, 255274459018, 1463246226849, 8387401847558, 48077013831427, 275579886633162, 1579637913256745

Offset

0,2

Comments

Fourth binomial transform of A038754, binomial transform of A140766.

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (8,-13).

Formula

a(n) = 8*a(n-1)-13(n-2) for n > 1; a(0) = 1, a(1) = 6.

G.f.: (1-2*x)/(1-8*x+13*x^2). - Klaus Brockhaus, Jun 19 2009

a(n) = A153594(n+1)-2*A153594(n). - R. J. Mathar, Feb 04 2021

Maple

seq(expand(((2+sqrt(3))*(4+sqrt(3))^n-(2-sqrt(3))*(4-sqrt(3))^n)/sqrt(12)), n = 0 .. 20) # Emeric Deutsch, Jun 20 2009

Mathematica

LinearRecurrence[{8, -13}, {1, 6}, 30] (* Harvey P. Dale, Jun 01 2016 *)

Prog

(PARI) F=nfinit(x^2-3); for(n=0, 20, print1(nfeltdiv(F, ((2+x)*(4+x)^n-(2-x)*(4-x)^n), (2*x))[1], ", ")) \\ Klaus Brockhaus, Jun 19 2009

Crossrefs

Cf. A038754, A140766.

Sequence in context: A081105 A079027 A289784 * A121838 A242629 A001109

Adjacent sequences: A161724 A161725 A161726 * A161728 A161729 A161730

Keyword

nonn,easy

Author

Al Hakanson (hawkuu(AT)gmail.com), Jun 17 2009

Extensions

Extended beyond a(6) by Klaus Brockhaus and Emeric Deutsch, Jun 19 2009

Edited by Klaus Brockhaus, Jul 05 2009

Status

approved