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%I #7 Aug 18 2018 11:27:35
%S 0,1,11,3,13,5,15,7,17,9,19,119,39,139,59,159,79,179,99,199,1199,399,
%T 1399,599,1599,799,1799,999,1999,11999,3999,13999,5999,15999,7999,
%U 17999,9999,19999,119999,39999,139999,59999,159999,79999,179999,99999,199999,1199999,399999
%N Expansion of x*(1 + 2*x*(5 - 4*x)*(1 + x^2)*(1 + x^4))/((1 - x)*(1 - 10*x^9)).
%C a(n) is the smallest number whose sum of odd decimal digits is n.
%H <a href="/index/Di#digital">Index entries for sequences related to digital root, sum, etc.</a>
%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,0,0,10,-10).
%F G.f.: x*(1 + 2*x*(5 - 4*x)*(1 + x^2)*(1 + x^4))/((1 - x)*(1 - 10*x^9)).
%F a(n) = a(n-1) + 10*a(n-9) - 10*a(n-10).
%t CoefficientList[Series[x (1 + 2 x (5 - 4 x) (1 + x^2) (1 + x^4))/((1 - x) (1 - 10 x^9)), {x, 0, 48}], x]
%t LinearRecurrence[{1, 0, 0, 0, 0, 0, 0, 0, 10, -10}, {0, 1, 11, 3, 13, 5, 15, 7, 17, 9}, 49]
%Y Cf. A051885, A071649.
%K nonn,base,easy
%O 0,3
%A _Ilya Gutkovskiy_, Aug 15 2018