OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (13,-40).
FORMULA
a(n) = (8^(n+1) - 5^(n+1))/3. - Lambert Klasen (lambert.klasen(AT)gmx.net), Feb 05 2005
a(0)=1, a(n) = 8*a(n-1) + 5^n. - Vincenzo Librandi, Feb 09 2011
a(0)=1, a(1)=13, a(n) = 13*a(n-1) - 40*a(n-2). - Harvey P. Dale, Feb 02 2015
E.g.f.: (1/3)*(-5*exp(5*x) + 8*exp(8*x)). - G. C. Greubel, Nov 09 2024
MATHEMATICA
Table[(8^(n+1)-5^(n+1))/3, {n, 0, 30}] (* Vladimir Joseph Stephan Orlovsky, Feb 01 2011 *)
CoefficientList[Series[1/((1-5x)(1-8x)), {x, 0, 30}], x] (* or *) LinearRecurrence[ {13, -40}, {1, 13}, 30] (* Harvey P. Dale, Feb 02 2015 *)
PROG
(PARI) Vec(1/((1-5*x)*(1-8*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012
(Magma) [n le 2 select 13^(n-1) else 13*Self(n-1) -40*Self(n-2): n in [1..31]]; // G. C. Greubel, Nov 09 2024
(SageMath)
A016162=BinaryRecurrenceSequence(13, -40, 1, 13)
[A016162(n) for n in range(31)] # G. C. Greubel, Nov 09 2024
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved