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%I #20 Feb 25 2021 02:03:27
%S 0,1,10,101,2010,10201,303010,1040201,40703010,107050201,5140803010,
%T 11112050201,625200803010,1162613050201,74146210803010,
%U 122513313050201,8639754210803010,12992793413050201,993903355210803010
%N 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.
%C 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).
%C 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).
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,201,0,-10100,0,9900).
%F 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.
%F From _R. J. Mathar_, Feb 11 2010: (Start)
%F a(n) = 201*a(n-2) - 10100*a(n-4) + 9900*a(n-6).
%F G.f.: x^2*(-1-10*x+100*x^2)/((x-1)*(1+x)*(90*x^2-1)*(110*x^2-1)). (End)
%e In pairs:
%e 0, 1;
%e 10, 101;
%e 2010, 10201;
%e 303010, 1040201;
%e 40703010, 107050201;
%e 5140803010, 11112050201;
%Y Cf. A162741, A161999, A007318, A000045.
%K nonn,base,less
%O 1,3
%A _Mark Dols_, Jul 14 2009
%E More terms from _R. J. Mathar_, Feb 11 2010
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