OFFSET
1,3
COMMENTS
Sum of pairs also (consecutive) cumulative sum of 110^n (or numerators of 1/110^1 + 1/110^2 + ... + 1/110^n, representing fraction 1/109).
Difference of pairs also cumulative sum of 90^n (or numerators of 1/90^1 + 1/90^2 + ... + 1/90^n, representing fraction 1/89).
LINKS
Index entries for linear recurrences with constant coefficients, signature (0,201,0,-10100,0,9900).
FORMULA
For n even: a(n) = 100*a(n-2)+10*a(n-1), for n odd: a(n) = 100*a(n-2)+10*a(n-3)+1; with a(0)=0, a(1)=1.
From R. J. Mathar, Feb 11 2010: (Start)
a(n) = 201*a(n-2) - 10100*a(n-4) + 9900*a(n-6).
G.f.: x^2*(-1-10*x+100*x^2)/((x-1)*(1+x)*(90*x^2-1)*(110*x^2-1)). (End)
EXAMPLE
In pairs:
0, 1;
10, 101;
2010, 10201;
303010, 1040201;
40703010, 107050201;
5140803010, 11112050201;
CROSSREFS
KEYWORD
nonn,base,less
AUTHOR
Mark Dols, Jul 14 2009
EXTENSIONS
More terms from R. J. Mathar, Feb 11 2010
STATUS
approved