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

Author

Wolfdieter Lang, Jul 11 2018

Keywords

• nonn
• easy

Comments

The other part of this bisection is given in A316708.

Links

• Index entries for sequences related to Chebyshev polynomials.
• Index entries for linear recurrences with constant coefficients, signature (34,-1).

Crossrefs

Cf. A000129, A001653, A029547, A316708.

Programs

PARI

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

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).