login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A016162
Expansion of 1/((1-5*x)*(1-8*x)).
7
1, 13, 129, 1157, 9881, 82173, 673009, 5462197, 44088201, 354658733, 2847035489, 22825112037, 182845036921, 1463980998493, 11717951503569, 93774129606677, 750345624744041, 6003527937405453, 48032038196509249
OFFSET
0,2
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
Cf. A016161.
Sequence in context: A147669 A076457 A227749 * A155623 A023061 A255495
KEYWORD
nonn,easy
STATUS
approved