This site is supported by donations to The OEIS Foundation.

 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!)
 A111566 a(n) = ((1+sqrt(8))*(2+sqrt(2))^n+(1-sqrt(8))*(2-sqrt(2))^n)/2. 4
 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 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). O.g.f.: (1+2*x)/(1-4*x+2*x^2). a(n) = A007070(n) + 2*A007070(n-1). - R. J. Mathar, Apr 02 2008 a(n) = Sum_{k, 0<=k<=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:=PolynomialRing(Integers()); N:=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 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.

Last modified November 18 02:54 EST 2017. Contains 294840 sequences.