A161729 a(n) = ((4+sqrt(3))*(8+2*sqrt(3))^n-(4-sqrt(3))*(8-2*sqrt(3))^n)/(2*sqrt(3)).

1, 16, 204, 2432, 28304, 326400, 3750592, 43036672, 493555968, 5658988544, 64878906368, 743795097600, 8527018430464, 97754949812224, 1120674238611456, 12847530427547648, 147285426432966656, 1688495240694988800, 19357081676605554688, 221911554309549457408, 2544016621769302474752

Offset

0,2

Comments

Eighth binomial transform of A162466.

Links

Harvey P. Dale, Table of n, a(n) for n = 0..943

Index entries for linear recurrences with constant coefficients, signature (16,-52).

Formula

a(n) = 16*a(n-1) - 52(n-2) for n > 1; a(0) = 1, a(1) = 16.

G.f.: 1/(1 - 16*x + 52*x^2). - Klaus Brockhaus, Jun 19 2009

a(n) = 2^n*A153594(n). - M. F. Hasler, Dec 03 2014

E.g.f.: exp(8*x)*(3*cosh(2*sqrt(3)*x) + 4*sqrt(3)*sinh(2*sqrt(3)*x))/3. - Stefano Spezia, Dec 31 2022

Mathematica

Join[{a=1, b=16}, Table[c=16*b-52*a; a=b; b=c, {n, 40}]] (* Vladimir Joseph Stephan Orlovsky, Feb 08 2011 *)
LinearRecurrence[{16, -52}, {1, 16}, 20] (* Harvey P. Dale, Dec 23 2020 *)

Prog

(PARI) F=nfinit(x^2-3); for(n=0, 17, print1(nfeltdiv(F, ((4+x)*(8+2*x)^n-(4-x)*(8-2*x)^n), (2*x))[1], ", ")) \\ Klaus Brockhaus, Jun 19 2009
(PARI) Vec(1/(1-16*x+52*x^2)+O(x^25)) \\ M. F. Hasler, Dec 03 2014

Crossrefs

Cf. A162466, A161728, A153594.

Sequence in context: A144632 A221825 A238282 * A157707 A016217 A055758

Adjacent sequences: A161726 A161727 A161728 * A161730 A161731 A161732

Keyword

nonn,easy

Author

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

Extensions

Extended beyond a(5) by Klaus Brockhaus, Jun 19 2009

Edited by Klaus Brockhaus, Jul 05 2009, and M. F. Hasler, Dec 03 2014

Status

approved