This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A027973 a(n) = T(n,n) + T(n,n+1) + ... + T(n,2n), T given by A027960. 6
 1, 4, 9, 21, 46, 99, 209, 436, 901, 1849, 3774, 7671, 15541, 31404, 63329, 127501, 256366, 514939, 1033449, 2072676, 4154701, 8324529, 16673534, 33386671, 66837421, 133778524, 267724809, 535721061, 1071881326, 2144473299, 4290096449, 8582053396, 17167117141 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (3,-1,-2). FORMULA With a different offset: recurrence: a(-1)=a(0)=1 a(n+2)=a(n+1)+a(n)+2^n; formula: a(n-2) = floor(2^n-PHI^n) - (1-(-1)^n)/2. - Benoit Cloitre, Sep 02 2002 a(n) = A101220(4, 2, n+1) - A101220(4, 2, n). - Ross La Haye, Aug 05 2005 a(n) = 2*a(n-1) + Fibonacci(n+1) - Fibonacci(n-3) for n>=1; a(0)=1. - Emeric Deutsch, Nov 29 2006 O.g.f.: 4/(1-2*x) - (x+3)/(1-x-x^2). - R. J. Mathar, Nov 23 2007 a(n) = 2^(n+2) + F(n) - F(n+4) with F(n)=A000045(n). - Johannes W. Meijer, Aug 15 2010 Eigensequence of an infinite lower triangular matrix with the Lucas series (1, 3, 4, 7,...) as the left border the rest ones. - Gary W. Adamson, Jan 30 2012 a(n) = 2^n - Lucas(n) for n>1. - Vincenzo Librandi, May 05 2017 MAPLE with(combinat): a[0]:=1: for n from 1 to 30 do a[n]:=2*a[n-1]+fibonacci(n+1)-fibonacci(n-3) od: seq(a[n], n=0..30); # Emeric Deutsch, Nov 29 2006 MATHEMATICA Table[2^n - LucasL[n], {n, 2, 50}] (* Vincenzo Librandi, May 05 2017 *) PROG (MAGMA) [2^n-Lucas(n): n in [2..40]]; // Vincenzo Librandi, May 05 2017 (PARI) vector(40, n, f=fibonacci; 2^(n+1) - f(n+2) - f(n) ) \\ G. C. Greubel, Sep 26 2019 (Sage) [2^(n+2) - lucas_number2(n+2, 1, -1) for n in (0..40)] # G. C. Greubel, Sep 26 2019 (GAP) List([0..40], n-> 2^(n+2) - Lucas(1, -1, n+2)[2]); # G. C. Greubel, Sep 26 2019 CROSSREFS Cf. A000032, A000045, A027960. Sequence in context: A048638 A144527 A117880 * A103040 A084861 A122498 Adjacent sequences:  A027970 A027971 A027972 * A027974 A027975 A027976 KEYWORD nonn AUTHOR 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.

Last modified October 16 13:51 EDT 2019. Contains 328093 sequences. (Running on oeis4.)