OFFSET
0,1
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000 (terms 0..144 from Vincenzo Librandi)
Index entries for linear recurrences with constant coefficients, signature (10,-17).
FORMULA
a(n) = ((5 + sqrt(18))*(5 + sqrt(8))^n + (5 - sqrt(18))*(5 - sqrt(8))^n)/2.
G.f.: (5-13*x)/(1-10*x+17*x^2).
E.g.f.: exp(5*x)*(5*cosh(2*sqrt(2)*x) + 3*sqrt(2)*sinh(2*sqrt(2)*x)). - G. C. Greubel, Aug 11 2017
a(n) = (1/2)*Sum_{k=0..n} binomial(n,k)*2^(n-k)*(3*Q(2*k+1) + 2*Q(2*k)), where Q(n) are the Pell-Lucas numbers (A002203). - G. C. Greubel, Apr 21 2020
MAPLE
seq(coeff(series( (5-13*x)/(1-10*x+17*x^2) , x, n+1), x, n), n = 0..25); # G. C. Greubel, Apr 21 2020
MATHEMATICA
CoefficientList[Series[(5 -13z)/(1 -10z +17z^2), {z, 0, 25}], z] (* Vladimir Joseph Stephan Orlovsky, Jun 12 2011 *)
LinearRecurrence[{10, -17}, {5, 37}, 25] (* G. C. Greubel, Aug 11 2017 *)
PROG
(Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((5+3*r)*(5+2*r)^n+(5-3*r)*(5-2*r)^n)/2: n in [0..18] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Aug 24 2009
(PARI) my(x='x+O('x^25)); Vec((5-13*x)/(1-10*x+17*x^2)) \\ G. C. Greubel, Aug 11 2017
(Sage)
def A164595_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( (5-13*x)/(1-10*x+17*x^2) ).list()
A164595_list(25) # G. C. Greubel, Apr 21 2020
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Al Hakanson (hawkuu(AT)gmail.com), Aug 17 2009
EXTENSIONS
Extended by Klaus Brockhaus and R. J. Mathar, Aug 24 2009
STATUS
approved