A161007 a(n+1) = 2*a(n) + 16*a(n-1), a(0)=0, a(1)=1.

0, 1, 2, 20, 72, 464, 2080, 11584, 56448, 298240, 1499648, 7771136, 39536640, 203411456, 1039409152, 5333401600, 27297349632, 139929124864, 716615843840, 3672097685504, 18810048872448, 96373660712960, 493708103385088, 2529394778177536, 12958119210516480

Offset

0,3

Links

Colin Barker, Table of n, a(n) for n = 0..1000

J. Borowska, L. Lacinska, Recurrence form of determinant of a heptadiagonal symmetric Toeplitz matrix, J. Appl. Math. Comp. Mech. 13 (2014) 19-16, remark 2 for permanent of tridiagonal Toeplitz matrices a=2, b=4.

Index entries for linear recurrences with constant coefficients, signature (2,16).

Formula

a(n) = ((1+sqrt(17))^n - (1-sqrt(17))^n)/(2*sqrt(17)).

Limit_{n -> oo} a(n+1)/a(n) = 1 + sqrt(17).

G.f.: x / (1 - 2*x - 16*x^2). - Colin Barker, Jul 01 2015

a(n) = 2^(n-1)*A006131(n-1). - R. J. Mathar, Mar 08 2021

a(n) = (4*i)^n*ChebyshevU(n, -i/4). - G. C. Greubel, Oct 15 2022

Mathematica

LinearRecurrence[{2, 16}, {0, 1}, 50] (* T. D. Noe, Nov 07 2011 *)

Prog

(PARI) concat(0, Vec(-x/(16*x^2+2*x-1) + O(x^40))) \\ Colin Barker, Jul 01 2015
(Magma) [n le 2 select n-1 else 2*(Self(n-1) +8*Self(n-2)): n in [1..41]]; // G. C. Greubel, Oct 15 2022
(SageMath)
A161007=BinaryRecurrenceSequence(2, 16, 0, 1)
[A161007(n) for n in range(41)] # G. C. Greubel, Oct 15 2022

Crossrefs

Cf. A006131, A010473 (sqrt(17)).

Sequence in context: A003283 A259110 A135188 * A331760 A098077 A279264

Adjacent sequences: A161004 A161005 A161006 * A161008 A161009 A161010

Keyword

nonn,easy

Author

Sture Sjöstedt, Jun 02 2009

Status

approved