login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A164038 Expansion of (5-19*x)/(1-10*x+23*x^2). 3
5, 31, 195, 1237, 7885, 50399, 322635, 2067173, 13251125, 84966271, 544886835, 3494644117, 22414043965, 143763624959, 922113238395, 5914569009893, 37937085615845, 243335768930911, 1560804720144675, 10011324516035797 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Binomial transform of A161731 without initial 1. Fifth binomial transform of A164095. Inverse binomial transform of A164110.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000 (terms 0..100 from Vincenzo Librandi)

Index entries for linear recurrences with constant coefficients, signature (10,-23).

FORMULA

a(n) = 10*a(n-1) - 23*a(n-2) for n > 1; a(0) = 5, a(1) = 31.

G.f.: (5-19*x)/(1-10*x+23*x^2).

a(n) = ((5+3*sqrt(2))*(5+sqrt(2))^n + (5-3*sqrt(2))*(5-sqrt(2))^n)/2.

E.g.f: (5*cosh(sqrt(2)*x) + 3*sqrt(2)*sinh(sqrt(2)*x))*exp(5*x). - G. C. Greubel, Sep 08 2017

MAPLE

a:=series((5-19*x)/(1-10*x+23*x^2), x=0, 20): seq(coeff(a, x, n), n=0..19); # Paolo P. Lava, Mar 28 2019

MATHEMATICA

LinearRecurrence[{10, -23}, {5, 31}, 50] (* or *) CoefficientList[Series[(5 - 19*x)/(1 - 10*x + 23*x^2), {x, 0, 50}], x] (* G. C. Greubel, Sep 08 2017 *)

PROG

(MAGMA) Z<x>:= PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((5+3*r)*(5+r)^n+(5-3*r)*(5-r)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Aug 10 2009

(PARI) Vec((5-19*x)/(1-10*x+23*x^2)+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012

CROSSREFS

Cf. A161731, A164095, A164110.

Sequence in context: A015540 A014987 A108079 * A260782 A084235 A288688

Adjacent sequences:  A164035 A164036 A164037 * A164039 A164040 A164041

KEYWORD

nonn,easy

AUTHOR

Al Hakanson (hawkuu(AT)gmail.com), Aug 08 2009

EXTENSIONS

Edited and extended beyond a(5) by Klaus Brockhaus, Aug 10 2009

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 February 20 07:54 EST 2020. Contains 332069 sequences. (Running on oeis4.)