A316709 Bisection of the odd-indexed Pell numbers A001853: part 2.

5, 169, 5741, 195025, 6625109, 225058681, 7645370045, 259717522849, 8822750406821, 299713796309065, 10181446324101389, 345869461223138161, 11749380235262596085, 399133058537705128729, 13558774610046711780701, 460599203683050495415105, 15646814150613670132332869, 531531081917181734003902441, 18056409971033565286000350125

Offset

0,1

Comments

The other part of this bisection is given in A316708.

Links

Table of n, a(n) for n=0..18.

Index entries for sequences related to Chebyshev polynomials.

Index entries for linear recurrences with constant coefficients, signature (34,-1).

Formula

a(n) = Pell(4*n+3) = A000129(4*n+3) = A001653(2*(n+1)), n >= 0.

a(n) = 34*a(n-1) - a(n-2), with a(-1) = and a(0) = 5.

a(n) = 5*S(n, 34) - S(n-1, 34), where the Chebyshev polynomial S(n, 34) = A029547(n), n >= 0, with S(-1, x) = 0.

G.f.: (5 - x)/(1- 34*x + x^2).

Prog

(PARI) x='x+O('x^99); Vec((5-x)/(1-34*x+x^2)) \\ Altug Alkan, Jul 11 2018

Crossrefs

Cf. A000129, A001653, A029547, A316708.

Sequence in context: A229524 A288352 A301949 * A293953 A264013 A326555

Adjacent sequences: A316706 A316707 A316708 * A316710 A316711 A316712

Keyword

nonn,easy

Author

Wolfdieter Lang, Jul 11 2018

Status

approved