OFFSET
1,1
LINKS
Index entries for linear recurrences with constant coefficients, signature (110,-1000).
FORMULA
a(n) = 10^(2*n) + 10^(n-1). The digits from the left to the right: number 1, n times 0, number 1, and (n-1) times 0.
From Chai Wah Wu, Jun 20 2016: (Start)
a(n) = 110*a(n-1) - 1000*a(n-2) for n > 2.
G.f.: x*(101 - 1100*x)/((1 - 10*x)*(1 - 100*x)). (End)
E.g.f.: (-11 + exp(10*x) + 10*exp(100*x))/10. - Ilya Gutkovskiy, Jun 21 2016
MATHEMATICA
Table[FromDigits@ IntegerDigits[2^(2 n) + 2^(n - 1), 2], {n, 12}] (* or *)
Rest@ CoefficientList[Series[x (101 - 1100 x)/((1 - 10 x) (1 - 100 x)), {x, 0, 12}], x] (* Michael De Vlieger, Jun 21 2016 *)
PROG
(PARI) x='x+O('x^50); Vec(x*(101 - 1100*x)/((1 - 10*x)*(1 - 100*x))) \\ G. C. Greubel, Sep 15 2017
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
Jaroslav Krizek, Aug 14 2009
EXTENSIONS
Edited by Charles R Greathouse IV, Oct 12 2009
STATUS
approved