0,1

Also gives the number of points of period n in the subshift of finite type corresponding to the square matrix A=[1,2;1,0] (this is then given by trace(A^n)). - Thomas Ward (t.ward(AT)uea.ac.uk), Mar 07 2001

Sequence is identical to its signed inverse binomial transform. - Paul Curtz (bpcrtz(AT)free.fr), Jul 11 2008

G. Everest, A. van der Poorten, I. Shparlinski and T. Ward, Recurrence Sequences, Amer. Math. Soc., 2003; see esp. pp. 180, 255.

Horadam, A. F. ``Jacobsthal and Pell Curves.'' Fib. Quart. 26, 79-83, 1988.

Horadam, A. F. ``Jacobsthal Representation Numbers.'' Fib Quart. 34, 40-54, 1996.

Lind and Marcus, An Introduction to Symbolic Dynamics and Coding, Cambridge University Press, 1995. (General material on subshifts of finite type)

T. D. Noe, Table of n, a(n) for n=0..200

Y. Puri and T. Ward, Arithmetic and growth of periodic orbits, J. Integer Seqs., Vol. 4 (2001), #01.2.1.

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

Index entries for sequences related to Chebyshev polynomials.

a(n+1) = 2 * a(n) - (-1)^n * 3.

a(n) = 2^n + (-1)^n. G.f.: (2-x)/(1-x-2*x^2). - Len Smiley (smiley(AT)math.uaa.alaska.edu), Dec 07 2001

E.g.f.: exp(x)+exp(-2x) produces a signed version. - Paul Barry (pbarry(AT)wit.ie), Apr 27 2003

a(n+1)=Sum{k=0..floor(n/2), binomial(n-1, 2k)3^(2k)/2^(n-2)}. - Paul Barry (pbarry(AT)wit.ie), Feb 21 2003

0, 1, 5, 7 ... is 2^n-2*0^n+(-1)^n, the 2nd inverse binomial transform of (2^n-1)^2 (A060867) - Paul Barry (pbarry(AT)wit.ie), Sep 05 2003

a(n)=2T(n, i/(2sqrt(2)))(-isqrt(2))^n with i^2=-1 - Paul Barry (pbarry(AT)wit.ie), Nov 17 2003

a(n)=(A078008(n)+A001045(n+1)) - Paul Barry (pbarry(AT)wit.ie), Feb 12 2004

a(n)=2*A001045(n+1)-A001045(n) - Paul Barry (pbarry(AT)wit.ie), Mar 22 2004

a(0)=2, a(1)=1, a(n)=a(n-1)+2*a(n-2) for n>1 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 07 2006

a(2n+1)=Product(d divides 2n+1, cyclotomic(d,2)). a(2^k*(2n+1))=Product(d divides 2n+1,cyclotomic(2d,2^(2^k))) - Miklos Kristof (kristmikl(AT)freemail.hu), Mar 12 2007

Cf. A001045 A019322 A066845.

Sequence in context: A002251 A093545 A005297 this_sequence A088014 A059274 A082635

Adjacent sequences: A014548 A014549 A014550 this_sequence A014552 A014553 A014554

nonn,nice

Eric Weisstein (eric(AT)weisstein.com)

More terms from Patrick De Geest (pdg(AT)worldofnumbers.com), Jun 15 1998.