0,1

a(n) gives the general (positive integer) solution of the Pell equation a^2 - 221*b^2 =+4 with companion sequence b(n)=A078364(n-1), n>=1.

O. Perron, "Die Lehre von den Kettenbruechen, Bd.I", Teubner, 1954, 1957 (Sec. 30, Satz 3.35, p. 109 and table p. 108).

Index entries for sequences related to linear recurrences with constant coefficients

Tanya Khovanova, Recursive Sequences

Index entries for recurrences a(n) = k*a(n - 1) +/- a(n - 2)

Index entries for sequences related to Chebyshev polynomials.

a(n)=15*a(n-1)-a(n-2), n >= 1; a(-1)=15, a(0)=2.

a(n) = S(n, 15) - S(n-2, 15) = 2*T(n, 15/2) with S(n, x) := U(n, x/2), S(-1, x) := 0, S(-2, x) := -1. S(n, 15)=A078364(n). U-, resp. T-, are Chebyshev's polynomials of the second, resp. first, case. See A049310 and A053120.

G.f.: (2-15*x)/(1-15*x+x^2).

a(n) = ap^n + am^n, with ap := (15+sqrt(221))/2 and am := (15-sqrt(221))/2.

a(n)=(15/2)*[15/2+(1/2)*sqrt(221)]^n-(1/2)*[15/2+(1/2)*sqrt(221)]^n*sqrt(221)+(1/2)*sqrt(221) *[15/2-(1/2)*sqrt(221)]^n+(15/2)*[15/2-(1/2)*sqrt(221)]^n, with n>=0 - Paolo P. Lava (ppl(AT)spl.at), Jun 19 2008

a[0] = 2; a[1] = 15; a[n_] := 15a[n - 1] - a[n - 2]; Table[ a[n], {n, 0, 15}] (from Robert G. Wilson v Jan 30 2004)

sage: [lucas_number2(n, 15, 1) for n in xrange(0, 20)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 26 2008

a(n)=sqrt(4 + 221*A078364(n-1)^2), n>=1, (Pell equation d=221, +4).

Cf. A077428, A078355 (Pell +4 equations).

Sequence in context: A087962 A140054 A099085 this_sequence A145168 A090301 A097628

Adjacent sequences: A078362 A078363 A078364 this_sequence A078366 A078367 A078368

nonn,easy

Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Nov 29 2002