OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..300
Index entries for linear recurrences with constant coefficients, signature (8,-9).
FORMULA
From Philippe Deléham and Klaus Brockhaus, Nov 05 2008: (Start)
a(n) = 8*a(n-1) - 9*a(n-2) with a(0)=1, a(1)=4.
G.f.: (1-4*x)/(1-8*x+9*x^2). (End)
a(n) = (Sum_{k=0..n} A098158(n,k)*4^(2*k)*7^(n-k))/4^n. - Philippe Deléham, Nov 06 2008
E.g.f.: exp(4*x)*cosh(sqrt(7)*x). - G. C. Greubel, Jan 08 2020
MAPLE
seq(coeff(series((1-4*x)/(1-8*x+9*x^2), x, n+1), x, n), n = 0..25); # G. C. Greubel, Jan 08 2020
MATHEMATICA
LinearRecurrence[{8, -9}, {1, 4}, 25] (* G. C. Greubel, Jan 08 2020 *)
PROG
(Magma) Z<x>:= PolynomialRing(Integers()); N<r7>:=NumberField(x^2-7); S:=[ ((4+r7)^n+(4-r7)^n)/2: n in [0..20] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Nov 05 2008
(PARI) my(x='x+O('x^25)); Vec((1-4*x)/(1-8*x+9*x^2)) \\ G. C. Greubel, Jan 08 2020
(Sage)
def A146964_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( (1-4*x)/(1-8*x+9*x^2) ).list()
A146964_list(25) # G. C. Greubel, Jan 08 2020
(GAP) a:=[1, 4];; for n in [3..25] do a[n]:=8*a[n-1]-9*a[n-2]; od; a; # G. C. Greubel, Jan 08 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Al Hakanson (hawkuu(AT)gmail.com), Nov 03 2008
EXTENSIONS
Extended beyond a(7) by Klaus Brockhaus, Nov 05 2008
Edited by Klaus Brockhaus, Jul 16 2009
STATUS
approved