OFFSET
0,2
COMMENTS
Binomial transform of A152056. Tenth binomial transform of powers of 3 interleaved with zeros.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..930
Index entries for linear recurrences with constant coefficients, signature (20,-97).
FORMULA
a(n) = ((10+sqrt(3))^n + (10-sqrt(3))^n)/2.
G.f.: (1-10*x)/(1-20*x+97*x^2).
MAPLE
seq(coeff(series((1-10*x)/(1-20*x+97*x^2), x, n+1), x, n), n = 0..20); # G. C. Greubel, Aug 27 2019
MATHEMATICA
LinearRecurrence[{20, -97}, {1, 10}, 20] (* G. C. Greubel, Aug 27 2019 *)
PROG
(Magma) [ n le 2 select 9*n-8 else 20*Self(n-1)-97*Self(n-2): n in [1..18] ];
(PARI) my(x='x+O('x^20)); Vec((1-10*x)/(1-20*x+97*x^2)) \\ G. C. Greubel, Aug 27 2019
(Sage)
def A162667_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P((1-10*x)/(1-20*x+97*x^2)).list()
A162667_list(20) # G. C. Greubel, Aug 27 2019
(GAP) a:=[1, 10];; for n in [3..20] do a[n]:=20*a[n-1]-97*a[n-2]; od; a; # G. C. Greubel, Aug 27 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Klaus Brockhaus, Jul 15 2009
STATUS
approved