VOOZH about

URL: https://oeis.org/A154244

⇱ A154244 - OEIS

login
A154244
a(n) = 6*a(n-1) - 2*a(n-2) for n>1; a(1)=1, a(2)=6.
11
1, 6, 34, 192, 1084, 6120, 34552, 195072, 1101328, 6217824, 35104288, 198190080, 1118931904, 6317211264, 35665403776, 201358000128, 1136817193216, 6418187159040, 36235488567808, 204576557088768, 1154988365396992
OFFSET
1,2
COMMENTS
Binomial transform of A126473.
lim_{n -> infinity} a(n)/a(n-1) = 3+sqrt(7) = 5.6457513110....
a(n) equals the number of words of length n-1 over {0,1,2,3,4,5} avoiding 01 and 02. - Milan Janjic, Dec 17 2015
LINKS
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).
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
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 *)
PROG
(Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=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
(SageMath) [lucas_number1(n, 6, 2) for n in range(1, 22)] # Zerinvary Lajos, Apr 22 2009
(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
CROSSREFS
Equals 1 followed by 2*A010913 (Pisot sequence E(3,17)).
Cf. A010465 (decimal expansion of square root of 7), A126473.
Sequence in context: A049608 A244937 A326656 * A273583 A126501 A391208
KEYWORD
nonn,easy
AUTHOR
Al Hakanson (hawkuu(AT)gmail.com), Jan 05 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
STATUS
approved