A016145 Expansion of g.f. 1/((1-3*x)*(1-10*x)).

1, 13, 139, 1417, 14251, 142753, 1428259, 14284777, 142854331, 1428562993, 14285688979, 142857066937, 1428571200811, 14285713602433, 142857140807299, 1428571422421897, 14285714267265691, 142857142801797073, 1428571428405391219, 14285714285216173657, 142857142855648520971

Offset

0,2

Links

Table of n, a(n) for n=0..20.

Index entries for linear recurrences with constant coefficients, signature (13,-30).

Formula

a(n) = (10^(n+1) - 3^(n+1))/7 = 10*a(n-1) + 3^n = 3*a(n-1) + 10^n. - Henry Bottomley, Jul 25 2001

a(n) = 13*a(n-1) - 30*a(n-2), n >= 2. - Vincenzo Librandi, Mar 14 2011

From Elmo R. Oliveira, Mar 08 2025: (Start)

E.g.f.: exp(3*x)*(10*exp(7*x) - 3)/7.

a(n) = A248226(n+1)/7. (End)

Mathematica

Join[{a=1, b=13}, Table[c=13*b-30*a; a=b; b=c, {n, 60}]] (* Vladimir Joseph Stephan Orlovsky, Feb 01 2011 *)
CoefficientList[Series[1/((1-3x)(1-10x)), {x, 0, 20}], x] (* or *) LinearRecurrence[{13, -30}, {1, 13}, 20] (* Harvey P. Dale, May 04 2018 *)

Crossrefs

Cf. A248226.

Sequence in context: A193700 A241631 A125425 * A351812 A300694 A193708

Adjacent sequences: A016142 A016143 A016144 * A016146 A016147 A016148

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved