login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A099140 a(n) = 4^n * T(n,3/2) where T is the Chebyshev polynomial of the first kind. 6
1, 6, 56, 576, 6016, 62976, 659456, 6905856, 72318976, 757334016, 7930904576, 83053510656, 869747654656, 9108115685376, 95381425750016, 998847258034176, 10460064284409856, 109539215284371456, 1147109554861899776 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

In general, r^n * T(n,(r+2)/r) has g.f. (1-(r+2)*x)/(1-2*(r+2)*x + r^2*x^2), e.g.f. exp((r+2)*x)*cosh(2*sqrt(r+1)*x), a(n) = Sum_{k=0..n} (r+1)^k*binomial(2n,2k) and a(n) = (1+sqrt(r+1))^(2n)/2 + (1-sqrt(r+1))^(2n)/2.

LINKS

Harvey P. Dale, Table of n, a(n) for n = 0..900

P. J. Szablowski, On moments of Cantor and related distributions, arXiv preprint arXiv:1403.0386 [math.PR], 2014.

Index entries for linear recurrences with constant coefficients, signature (12,-16).

FORMULA

G.f.: (1-6*x)/(1-12*x+16*x^2);

E.g.f.: exp(6*x)*cosh(2*sqrt(5)*x);

a(n) = 4^n * T(n, 6/4) where T is the Chebyshev polynomial of the first kind;

a(n) = Sum_{k=0..n} 5^k*binomial(2n, 2k);

a(n) = (1+sqrt(5))^(2n)/2 + (1-sqrt(5))^(2n)/2.

a(n) = a(0)=1, a(1)=6, 12*a(n-1) - 16*a(n-2) for n > 1. - Philippe Deléham, Sep 08 2009

MATHEMATICA

LinearRecurrence[{12, -16}, {1, 6}, 30] (* Harvey P. Dale, Oct 23 2012 *)

PROG

(PARI) a(n) = 4^n*polchebyshev(n, 1, 3/2); \\ Michel Marcus, Sep 08 2019

CROSSREFS

Cf. A001541, A081294, A083884, A090965, A099141, A099142.

Sequence in context: A181589 A093142 A092655 * A048348 A227384 A199755

Adjacent sequences:  A099137 A099138 A099139 * A099141 A099142 A099143

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Sep 30 2004

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 15 06:11 EST 2019. Contains 329144 sequences. (Running on oeis4.)