0,2

Generalized Fibonacci sequence.

Sqrt(26) = 10/2 + 10/101 + 10/(101*10301) + 10/(10301*1050601) + ... - Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 13 2008

S. Falcon & A. Plaza: The k-Fibonacci sequence and the Pascal 2-triangle, Chaos, Solitons & Fractals, 33 (2007)

S. Falcon & A. Plaza: On k-Fibonacci sequences and polynomials and their derivatives, Chaos, Solitons & Fractals (2007)

Tanya Khovanova, Recursive Sequences

Index entries for sequences related to Chebyshev polynomials.

a(n) = 10*a(n-1) + a(n-2), n>=1; a(-1):=0, a(0)=1.

G.f.: 1/(1-10*x-x^2).

a(n) = S(n, 10*I)*(-I)^n with I^2:=-1 and S(n, x)=U(n, x/2) Chebyshev's polynomials of the second kind. See A049310.

a(n) = (ap^(n+1) - am^(n+1))/(ap-am) with ap:= 5 + sqrt(26), am:= 5 - sqrt(26)=-1/ap.

a(n)=F(n, 10), the n-th Fibonacci polynomial evaluated at x=10. - T. D. Noe (noe(AT)sspectra.com), Jan 19 2006

a(n) = ((5+Sqrt[26])^n-(5-Sqrt[26])^n)/(2Sqrt[26]); a(n) = Sum[Binomial[n-1-i,i]*10^{n-1-2i}, {i,0,Floor[(n-1)/2]}] - Sergio Falcon (sfalcon(AT)dma.ulpgc.es), Sep 24 2007

a=0; lst={}; s=0; Do[a=s-(a-1); AppendTo[lst, a]; s+=a*10, {n, 3*4!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Oct 27 2009]

(Other) sage: [lucas_number1(n, 10, -1) for n in xrange(1, 19)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 26 2009]

Cf. A041040.

Cf. squares A099374.

Cf. A000045, A000129, A006190, A001076, A052918, A005668, A054413, A041025, A099371.

Sequence in context: A096883 A033128 A094945 this_sequence A163461 A081192 A108892

Adjacent sequences: A041038 A041039 A041040 this_sequence A041042 A041043 A041044

nonn,cofr,easy

N. J. A. Sloane (njas(AT)research.att.com).