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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)=2a(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

From Johannes W. Meijer, Aug 15 2010: (Start)

a(n) = 2^(n+2)+F(n)-F(n+4) with F(n)=A000045(n).

(End)

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

CROSSREFS

Sequence in context: A048638 A144527 A117880 * A103040 A084861 A122498

Adjacent sequences:  A027970 A027971 A027972 * A027974 A027975 A027976

KEYWORD

nonn

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified October 23 01:57 EDT 2018. Contains 316518 sequences. (Running on oeis4.)