0,1

a(n) gives the general (positive integer) solution of the Pell equation a^2 - 285*b^2 =+4 with companion sequence b(n)=A078366(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)=17*a(n-1)-a(n-2), n >= 1; a(-1)=17, a(0)=2.

a(n) = S(n, 17) - S(n-2, 17) = 2*T(n, 17/2) with S(n, x) := U(n, x/2), S(-1, x) := 0, S(-2, x) := -1. S(n, 17)=A078366(n). U-, resp. T-, are Chebyshev's polynomials of the second, resp. first, case. See A049310 and A053120.

G.f.: (2-17*x)/(1-17*x+x^2).

a(n) = ap^n + am^n, with ap := (17+sqrt(285))/2 and am := (17-sqrt(285))/2.

a[0] = 2; a[1] = 17; a[n_] := 17a[n - 1] - a[n - 2]; Table[ a[n], {n, 0, 15}] (from Robert G. Wilson v Jan 30 2004)

(PARI) a(n)=if(n<0, 0, subst(2*poltchebi(n), x, 17/2))

sage: [lucas_number2(n, 17, 1) for n in xrange(0, 20)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 26 2008

a(n)=sqrt(4 + 285*A078366(n-1)^2), n>=1, (Pell equation d=285, +4).

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

Sequence in context: A037896 A099714 A086534 this_sequence A090306 A007785 A128159

Adjacent sequences: A078364 A078365 A078366 this_sequence A078368 A078369 A078370

nonn,easy

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