A248163 Chebyshev's S polynomials (A049310) evaluated at 34/3 and multiplied by powers of 3 (A000244).

1, 34, 1147, 38692, 1305205, 44028742, 1485230383, 50101574344, 1690086454249, 57012025275370, 1923198081274339, 64875626535849196, 2188462519487403613, 73823845023749080078, 2490314568132082090135, 84006280711277049343888, 2833800713070230938880977, 95593167717986358477858226

Offset

0,2

Comments

This sequence appears in the solution for the curvature sequence of the touching circle and chord example given in A249457. See also the pair A249862(n) and a(n-1), with a(-1) = 0, for which details are given in A249862.

Links

Table of n, a(n) for n=0..17.

Index entries for linear recurrences with constant coefficients, signature (34,-9).

Formula

a(n) = 3^n*S(n, 34/3) with Chebyshev's S polynomial (for S see the coefficient triangle A049310).

O.g.f.: 1/(1 - 34*x + (3*x)^2).

a(n) = 34*a(n-1) - 9*a(n-2), a(-1) = 0, a(0) = 1 .

E.g.f.: exp(17*x)*(140*cosh(2*sqrt(70)*x) + 17*sqrt(70)*sinh(2*sqrt(70)*x))/140. - Stefano Spezia, Mar 24 2023

Mathematica

CoefficientList[Series[1 / (1 - 34 x + (3 x)^2), {x, 0, 40}], x] (* Vincenzo Librandi, Nov 08 2014 *)

Prog

(Magma) I:=[1, 34]; [n le 2 select I[n] else 34*Self(n-1) - 9*Self(n-2): n in [1..20]]; // Vincenzo Librandi, Nov 08 2014

Crossrefs

Cf. A049310, A000244, A249862, A249457.

Sequence in context: A170715 A170753 A218736 * A158696 A029547 A091761

Adjacent sequences: A248160 A248161 A248162 * A248164 A248165 A248166

Keyword

nonn,easy

Author

Wolfdieter Lang, Nov 07 2014

Extensions

a(16)-a(17) from Stefano Spezia, Mar 24 2023

Status

approved