A099856 Expansion of (1+3*x)/(1-3*x).

1, 6, 18, 54, 162, 486, 1458, 4374, 13122, 39366, 118098, 354294, 1062882, 3188646, 9565938, 28697814, 86093442, 258280326, 774840978, 2324522934, 6973568802, 20920706406, 62762119218, 188286357654, 564859072962, 1694577218886, 5083731656658, 15251194969974, 45753584909922

Offset: 0

Author

Paul Barry, Oct 28 2004

Keywords

• easy
• nonn

Comments

A099858 gives a Chebyshev transform. Binomial transform is A083420.

Hankel transform is 1, -18, 0, 0, 0, 0, 0, 0, 0, ... - Philippe Deléham, Dec 13 2011

Links

• Index entries for linear recurrences with constant coefficients, signature (3).

Crossrefs

Cf. A025192, A083420, A093561, A099858.

Programs

Mathematica

CoefficientList[Series[(1+3x)/(1-3x),{x,0,30}],x] (* or *) Join[{1}, NestList[3#&,6,30]] (* Harvey P. Dale, Nov 08 2011 *)

PARI

Vec((1+3*x)/(1-3*x) + O(x^40)) \\ Michel Marcus, Dec 11 2015

Formula

a(n) = 2*3^n - 0^n.

a(n) = A025192(n+1), n > 0. - R. J. Mathar, Sep 02 2008

a(n) = Sum_{k=0..n} A093561(n,k)*2^k. - Philippe Deléham, Dec 13 2011

From Elmo R. Oliveira, Aug 23 2024: (Start)

E.g.f.: 2*exp(3*x) - 1.

a(n) = 3*a(n-1) for n > 1. (End)

Extensions

a(26)-a(28) from Elmo R. Oliveira, Aug 23 2024