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

 

Logo

Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A054485 Expansion of (1+3*x)/(1-4*x+x^2). 4
1, 7, 27, 101, 377, 1407, 5251, 19597, 73137, 272951, 1018667, 3801717, 14188201, 52951087, 197616147, 737513501, 2752437857, 10272237927, 38336513851, 143073817477, 533958756057, 1992761206751, 7437086070947, 27755583077037 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 122-125, 194-196.

LINKS

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

I. Adler, Three Diophantine equations - Part II, Fib. Quart., 7 (1969), pp. 181-193.

E. I. Emerson, Recurrent Sequences in the Equation DQ^2=R^2+N, Fib. Quart., 7 (1969), pp. 231-242.

Tanya Khovanova, Recursive Sequences

Index entries for linear recurrences with constant coefficients, signature (4,-1).

FORMULA

a(n) = (7*((2+sqrt(3))^n - (2-sqrt(3))^n) - ((2+sqrt(3))^(n-1) - (2-sqrt(3))^(n-1)))/2*sqrt(3).

a(n) = 4*a(n-1) - a(n-2), a(0)=1, a(0)=7.

MATHEMATICA

LinearRecurrence[{4, -1}, {1, 7}, 40] (* Vincenzo Librandi, Jun 23 2012 *)

PROG

(MAGMA) I:=[1, 7]; [n le 2 select I[n] else 4*Self(n-1)-Self(n-2): n in[1..30]]; // Vincenzo Librandi, Jun 23 2012

(PARI) Vec((1+3*x)/(1-4*x+x^2) + O(x^30)) \\ Michel Marcus, Mar 20 2015

CROSSREFS

Cf. A054491.

Sequence in context: A282642 A185080 A006350 * A090856 A055917 A056120

Adjacent sequences:  A054482 A054483 A054484 * A054486 A054487 A054488

KEYWORD

easy,nonn

AUTHOR

Barry E. Williams, May 06 2000

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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified November 19 07:16 EST 2017. Contains 294916 sequences.