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A108981
a(n) = 3a(n-1) + 4a(n-2), a(0) = 1, a(1) = 5.
7
1, 5, 19, 77, 307, 1229, 4915, 19661, 78643, 314573, 1258291, 5033165, 20132659, 80530637, 322122547, 1288490189, 5153960755, 20615843021, 82463372083, 329853488333, 1319413953331, 5277655813325, 21110623253299
OFFSET
0,2
COMMENTS
The Hankel transform of this sequence is [1,-6,0,0,0,0,0,0,0,0,...]. - Philippe Deléham, Apr 15 2008
Let A be the Hessenberg matrix of order n, defined by: A[1,j]=1, A[i,i]:=-2, A[i,i-1]=-1, and A[i,j]=0 otherwise. Then, for n >= 1, a(n-1) = charpoly(A,2). - Milan Janjic, Jan 26 2010
FORMULA
Inverse binomial transform of A003948.
a(2n) = 4a(2n-1) - 1; a(2n+1) = 4a(2n) + 1.
O.g.f.: (1+2*x)/((1+x)(1-4*x)). - R. J. Mathar, Apr 02 2008
Sum_{k=0..n} a(k) = A037481(n+1). - Philippe Deléham, Apr 15 2008
MATHEMATICA
LinearRecurrence[{3, 4}, {1, 5}, 30] (* Harvey P. Dale, Feb 16 2014 *)
PROG
(PARI) Vec((1+2*x)/(1+x)/(1-4*x)+O(x^99)) \\ Charles R Greathouse IV, Jan 11 2012
(Magma) I:=[1, 5]; [n le 2 select I[n] else 3*Self(n-1)+4*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Feb 17 2014
CROSSREFS
Sequence in context: A275859 A323269 A268815 * A228678 A149771 A149772
KEYWORD
nonn,easy
AUTHOR
Philippe Deléham, Jul 23 2005
EXTENSIONS
Corrected by T. D. Noe, Nov 07 2006
Edited by N. J. A. Sloane at the suggestion of R. J. Mathar, Apr 14 2008
STATUS
approved