A162849 Pairs of numbers that add up to the 'backward decimal expansion' of fraction 1/109 and whose difference is the 'backward decimal expansion' of fraction 1/89.
0, 1, 10, 101, 2010, 10201, 303010, 1040201, 40703010, 107050201, 5140803010, 11112050201, 625200803010, 1162613050201, 74146210803010, 122513313050201, 8639754210803010, 12992793413050201, 993903355210803010
Offset: 1
Examples
In pairs:
0, 1;
10, 101;
2010, 10201;
303010, 1040201;
40703010, 107050201;
5140803010, 11112050201;
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)
Extensions
More terms from R. J. Mathar, Feb 11 2010
Comments