A154244 a(n) = 6*a(n-1) - 2*a(n-2) for n>1; a(1)=1, a(2)=6.
1, 6, 34, 192, 1084, 6120, 34552, 195072, 1101328, 6217824, 35104288, 198190080, 1118931904, 6317211264, 35665403776, 201358000128, 1136817193216, 6418187159040, 36235488567808, 204576557088768, 1154988365396992
Offset: 1
Links
- Vincenzo Librandi, Table of n, a(n) for n = 1..500
- Tomislav Doslic, Planar polycyclic graphs and their Tutte polynomials, Journal of Mathematical Chemistry, Volume 51, Issue 6, 2013, pp. 1599-1607. See Cor. 3.7(e).
- Index entries for linear recurrences with constant coefficients, signature (6,-2).
Crossrefs
Programs
-
Magma
Z
:=PolynomialRing(Integers()); N :=NumberField(x^2-7); S:=[ ((3+r)^n-(3-r)^n)/(2*r): n in [1..21] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jan 07 2009 -
Magma
I:=[1, 6]; [n le 2 select I[n] else 6*Self(n-1)-2*Self(n-2): n in [1..50]]; // Vincenzo Librandi, Feb 02 2012
-
Mathematica
a[n_]:=(MatrixPower[{{1,3},{1,5}},n].{{1},{1}})[[2,1]]; Table[a[n],{n,0,40}] (* Vladimir Joseph Stephan Orlovsky, Feb 19 2010 *) LinearRecurrence[{6, -2}, {1, 6}, 40] (* Vincenzo Librandi, Feb 02 2012 *) -
Maxima
a[1]:1$ a[2]:6$ a[n]:=6*a[n-1]-2*a[n-2]$ makelist(a[n], n, 1, 21); /* Bruno Berselli, May 30 2011 */
-
PARI
Vec(1/(1-6*x+2*x^2)+O(x^99)) \\ Charles R Greathouse IV, Dec 28 2011
-
Sage
[lucas_number1(n,6,2) for n in range(1, 22)] # Zerinvary Lajos, Apr 22 2009
Formula
a(n) = ((3 + sqrt(7))^n - (3 - sqrt(7))^n)/(2*sqrt(7)).
G.f.: x/(1-6*x+2*x^2). - Philippe Deléham, Jan 06 2009
Extensions
Extended beyond a(7) by Klaus Brockhaus, Jan 07 2009
Edited by Klaus Brockhaus, Oct 06 2009
Name (corrected) from Philippe Deléham, Jan 06 2009
Comments