0,3

Any k in the sequence is followed by 5*k + 2sqrt{2(3*k^2 - 1)}. Gives solutions for x in 3*x^2 - 2*y^2 = 1. Corresponding y is given by A054320(n).

a(n) = L(n-1,10), where L is defined as in A108299; see also A054320 for L(n,-10). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jun 01 2005

Number of 01-avoiding words of length n on alphabet {0,1,2,3,4,5,6,7,8,9} which do not end in 0. - Tanya Khovanova (tanyakh(AT)yahoo.com), Jan 10 2007

a(n) = A138288(n-1) for n > 0. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Mar 12 2008

S. J. Cyvin and I. Gutman, Kekule structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (p. 283).

Index entries for sequences related to linear recurrences with constant coefficients

Tanya Khovanova, Recursive Sequences

Index entries for sequences related to Chebyshev polynomials.

a(n) = (3-sqrt(6))/6 * (5+2*sqrt(6))^n + (3+sqrt(6))/6 * (5-2*sqrt(6))^n.

a(n)={2*A031138(n) + 1}/3 = sqrt(2*A054320(n)^2 + 1)/3), n>=1.

a(n) = U(n-1, 5)-U(n-2, 5) = T(2*n-1, sqrt(3))/sqrt(3) with Chebyshev's U- and T- polynomials and U(-1, x) := 0, U(-2, x) := -1, T(-1, x) := x.

G.f.: (1-9*x)/(1-10*x+x^2).

For all members x of the sequence, 6*x^2 - 2 is a square. Lim. n -> Inf. a(n)/a(n-1) = 5 + 2*sqrt(6). - Gregory V. Richardson (omomom(AT)hotmail.com), Oct 10 2002

Let q(n, x)=sum(i=0, n, x^(n-i)*binomial(2*n-i, i)); then q(n, 8)=a(n+1) - Benoit Cloitre (benoit7848c(AT)orange.fr), Nov 10 2002

a(n)a(n+3) = 80 + a(n+1)a(n+2). - R. Stephan, May 29 2004

a[n_] := a[n] = 10a[n - 1] - a[n - 2]; a[0] = a[1] = 1; Table[ a[n], {n, 0, 20}]

(Other) sage: [lucas_number1(n, 10, 1)-lucas_number1(n-1, 10, 1) for n in xrange(0, 20)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 10 2009]

Cf. A054320, A031138.

Row 10 of array A094954.

First differences of A004189.

A072256(n)=sqrt(A046172(n)) [From Weisenhorn Paul (paulweisenhorn(AT)online.de), May 15 2009]

Sequence in context: A064616 A133486 A015584 this_sequence A138288 A059482 A109002

Adjacent sequences: A072253 A072254 A072255 this_sequence A072257 A072258 A072259

nonn

Lekraj Beedassy (blekraj(AT)yahoo.com), Jul 08 2002

Edited by Robert G. Wilson v (rgwv(AT)rgwv.com), Jul 17 2002