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

1,3

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

Table of n, a(n) for n=1..19.

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

Cf. A162741, A161999, A007318, A000045.

Sequence in context: A108892 A309802 A324083 * A041182 A036299 A061107

Adjacent sequences: A162846 A162847 A162848 * A162850 A162851 A162852

Keyword

nonn,base,less

Author

Mark Dols, Jul 14 2009

Extensions

More terms from R. J. Mathar, Feb 11 2010

Status

approved