A302556 Expansion of x*(1 + 2*x*(5 - 4*x)*(1 + x^2)*(1 + x^4))/((1 - x)*(1 - 10*x^9)).

0, 1, 11, 3, 13, 5, 15, 7, 17, 9, 19, 119, 39, 139, 59, 159, 79, 179, 99, 199, 1199, 399, 1399, 599, 1599, 799, 1799, 999, 1999, 11999, 3999, 13999, 5999, 15999, 7999, 17999, 9999, 19999, 119999, 39999, 139999, 59999, 159999, 79999, 179999, 99999, 199999, 1199999, 399999

Offset

0,3

Comments

a(n) is the smallest number whose sum of odd decimal digits is n.

Links

Table of n, a(n) for n=0..48.

Index entries for sequences related to digital root, sum, etc.

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,10,-10).

Formula

G.f.: x*(1 + 2*x*(5 - 4*x)*(1 + x^2)*(1 + x^4))/((1 - x)*(1 - 10*x^9)).

a(n) = a(n-1) + 10*a(n-9) - 10*a(n-10).

Mathematica

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]
LinearRecurrence[{1, 0, 0, 0, 0, 0, 0, 0, 10, -10}, {0, 1, 11, 3, 13, 5, 15, 7, 17, 9}, 49]

Crossrefs

Cf. A051885, A071649.

Sequence in context: A075023 A363099 A205960 * A088262 A110406 A237454

Adjacent sequences: A302553 A302554 A302555 * A302557 A302558 A302559

Keyword

nonn,base,easy

Author

Ilya Gutkovskiy, Aug 15 2018

Status

approved