login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A002534 a(n) = 2*a(n-1) + 9*a(n-2).
(Formerly M2058 N0814)
18
0, 1, 2, 13, 44, 205, 806, 3457, 14168, 59449, 246410, 1027861, 4273412, 17797573, 74055854, 308289865, 1283082416, 5340773617, 22229288978, 92525540509, 385114681820, 1602959228221, 6671950592822, 27770534239633, 115588623814664 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

For n>=2, a(n) equals the permanent of the (n-1)X(n-1) tridiagonal matrix with 2's along the main diagonal, and 3's along the superdiagonal and the subdiagonal. - John M. Campbell, Jul 19 2011

REFERENCES

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

A. Tarn, Approximations to certain square roots and the series of numbers connected therewith, Mathematical Questions and Solutions from the Educational Times, 1 (1916), 8-12.

LINKS

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

Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992.

Simon Plouffe, 1031 Generating Functions and Conjectures, Université du Québec à Montréal, 1992.

Albert Tarn, Approximations to certain square roots and the series of numbers connected therewith [Annotated scanned copy]

Index entries for linear recurrences with constant coefficients, signature (2, 9).

FORMULA

From Paul Barry, Sep 29 2004: (Start)

E.g.f.: exp(x)*sinh(sqrt(10)*x)/sqrt(10).

a(n) = Sum_{k=0..n} binomial(n, 2*k+1)*10^k. (End)

a(n) = ((1+sqrt(10))^n - (1-sqrt(10))^n)/(2*sqrt(10)). - Artur Jasinski, Dec 10 2006

G.f.: x/(1 - 2*x - 9*x^2) - Iain Fox, Jan 17 2018

MAPLE

A002534:=-z/(-1+2*z+9*z**2); # [Simon Plouffe in his 1992 dissertation.]

MATHEMATICA

Table[((1 + Sqrt[10])^n - (1 - Sqrt[10])^n)/(2 Sqrt[10]), {n, 0, 30}]] (* Artur Jasinski, Dec 10 2006 *)

LinearRecurrence[{2, 9}, {0, 1}, 30] (* T. D. Noe, Aug 18 2011 *)

PROG

(Sage) [lucas_number1(n, 2, -9) for n in xrange(0, 20)] # Zerinvary Lajos, Apr 22 2009

(MAGMA) [Ceiling(((1+Sqrt(10))^n-(1-Sqrt(10))^n)/(2*Sqrt(10))): n in [0..30]]; // Vincenzo Librandi, Aug 15 2011

(PARI) first(n) = Vec(x/(1 - 2*x - 9*x^2) + O(x^n), -n) \\ Iain Fox, Jan 17 2018

CROSSREFS

Sequence in context: A296807 A025194 A084156 * A212501 A117717 A176060

Adjacent sequences:  A002531 A002532 A002533 * A002535 A002536 A002537

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Johannes W. Meijer, Aug 18 2011

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 16 11:12 EDT 2019. Contains 324152 sequences. (Running on oeis4.)