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

 

Logo

Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS").
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A161947 a(n) = ((4+sqrt(2))*(5+sqrt(2))^n + (4-sqrt(2))*(5-sqrt(2))^n)/4. 2
2, 11, 64, 387, 2398, 15079, 95636, 609543, 3895802, 24938531, 159781864, 1024232427, 6567341398, 42116068159, 270111829436, 1732448726703, 11111915190002, 71272831185851, 457154262488464, 2932267507610067 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Fifth binomial transform of A135530.

LINKS

Muniru A Asiru, Table of n, a(n) for n = 0..252

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) = 2; a(1) = 11.

G.f.: (2-9*x)/(1-10*x+23*x^2).

MAPLE

seq(simplify(((4+sqrt(2))*(5+sqrt(2))^n+(4-sqrt(2))*(5-sqrt(2))^n)*1/4), n = 0 .. 20); # Emeric Deutsch, Jun 28 2009

MATHEMATICA

LinearRecurrence[{10, -23}, {2, 11}, 50] (* G. C. Greubel, Aug 17 2018 *)

Table[(((4+Sqrt[2])(5+Sqrt[2])^n)+((4-Sqrt[2])(5-Sqrt[2])^n))/4, {n, 0, 20}]//Simplify (* Harvey P. Dale, Mar 07 2020 *)

PROG

(MAGMA) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((4+r)*(5+r)^n+(4-r)*(5-r)^n)/4: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jul 01 2009

(GAP) a := [2, 11];; for n in [3..10^2] do a[n] := 10*a[n-1] - 23*a[n-2]; od; a; # Muniru A Asiru, Feb 02 2018

(PARI) x='x+O('x^30); Vec((2-9*x)/(1-10*x+23*x^2)) \\ G. C. Greubel, Aug 17 2018

CROSSREFS

Cf. A135530.

Sequence in context: A126745 A179120 A038725 * A001565 A199412 A074613

Adjacent sequences:  A161944 A161945 A161946 * A161948 A161949 A161950

KEYWORD

nonn

AUTHOR

Al Hakanson (hawkuu(AT)gmail.com), Jun 22 2009

EXTENSIONS

Edited and extended beyond a(4) by Klaus Brockhaus, Jul 01 2009

Extended by Emeric Deutsch, Jun 28 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 November 25 05:43 EST 2020. Contains 338617 sequences. (Running on oeis4.)