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
Links
- Index entries for linear recurrences with constant coefficients, signature (13,-30).
Crossrefs
Cf. A248226.
Programs
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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 *)
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)