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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A111566 a(n) = ((1+sqrt(8))*(2+sqrt(2))^n + (1-sqrt(8))*(2-sqrt(2))^n)/2. 5
1, 6, 22, 76, 260, 888, 3032, 10352, 35344, 120672, 412000, 1406656, 4802624, 16397184, 55983488, 191139584, 652591360, 2228086272, 7607162368, 25972476928, 88675582976, 302757378048, 1033678346240, 3529198628864 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Binomial transform of A048655: generalized Pellian with second term equal to 5.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (4,-2).

FORMULA

a(n) = 4*a(n-1) - 2*a(n-2), a(0) = 1, a(1) = 6.

Program "FAMP" returns: a(n) = A007052(n) - A006012(n) + A111567(n).

From R. J. Mathar, Apr 02 2008: (Start)

O.g.f.: (1+2*x)/(1-4*x+2*x^2).

a(n) = A007070(n) + 2*A007070(n-1). (End)

a(n) = Sum_{k=0..n} A207543(n,k)*2^k. - Philippe Deléham, Feb 25 2012

a(n) = 4*A007070(n) - A007052(n+1). - Yuriy Sibirmovsky, Sep 13 2016

MATHEMATICA

LinearRecurrence[{4, -2}, {1, 6}, 30] (* Harvey P. Dale, Jan 31 2015 *)

PROG

Floretion Algebra Multiplication Program, FAMP Code: 1vesseq[K*J] with K = + .5'i + .5'j + .5k' + .5'kk' and J = + .5i' + .5j' + 2'kk' + .5'ki' + .5'kj'.

(MAGMA) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((1+2*r)*(2+r)^n+(1-2*r)*(2-r)^n)/2: n in [0..23] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jul 27 2009

(PARI) x='x+O('x^30); Vec((1+2*x)/(1-4*x+2*x^2)) \\ G. C. Greubel, Jan 27 2018

CROSSREFS

Cf. A007052, A006012, A111567, A007070.

Sequence in context: A159555 A032195 A217530 * A200052 A051945 A253070

Adjacent sequences:  A111563 A111564 A111565 * A111567 A111568 A111569

KEYWORD

easy,nonn

AUTHOR

Creighton Dement, Aug 06 2005

EXTENSIONS

Edited by N. J. A. Sloane, Jul 27 2009 using new definition from Al Hakanson (hawkuu(AT)gmail.com)

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 17 15:12 EST 2018. Contains 317276 sequences. (Running on oeis4.)