OFFSET
0,3
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (0,11,0,-10).
FORMULA
For n > 0, a(2*n+1) is represented as a string of n 2's and a(2*n) as a string of (n-1) 1's followed by a 2.
From Colin Barker, Apr 01 2016: (Start)
a(n) = (6+10*(-1)^n+10^(1/2*(-1+n))*(2-2*(-1)^n+sqrt(10)+(-1)^n*sqrt(10)))/18.
a(n) = (10^(n/2)+8)/9 for n even.
a(n) = (2^((n+1)/2)*5^((n-1)/2)-2)/9 for n odd.
a(n) = 11*a(n-2)-10*a(n-4) for n>3.
G.f.: (1-9*x^2+2*x^3) / ((1-x)*(1+x)*(1-10*x^2)).
(End)
EXAMPLE
a(8)= 1112 because A078008(8) = 86 (in base 10) = 64 + 16 + 4 + 2 = 1*(4^3) + 1*(4^2) + 1*(4^1) + 2.
PROG
(PARI) Vec((1-9*x^2+2*x^3)/((1-x)*(1+x)*(1-10*x^2)) + O(x^30)) \\ Colin Barker, Apr 01 2016
CROSSREFS
KEYWORD
easy,base,nonn
AUTHOR
Paul Barry, Mar 12 2004
STATUS
approved