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A211072 Sum of numbers with no '0' decimal digits whose sum of digits equals n.

%I A211072 #42 Jul 06 2021 15:59:35
%S A211072 0,1,13,147,1625,17891,196833,2165227,23817625,261994131,2881935943,
%T A211072 31701296375,348714262017,3835856884757,42194425724149,
%U A211072 464138682802857,5105525508895321,56160780576260645,617768586100819485,6795454444489330049,74749998860563784655
%N A211072 Sum of numbers with no '0' decimal digits whose sum of digits equals n.
%C A211072 Different from A016135.
%H A211072 Alois P. Heinz, <a href="/A211072/b211072.txt">Table of n, a(n) for n = 0..961</a> (terms n = 1..31 from Laurent Desnogues)
%H A211072 Project Euler, <a href="http://projecteuler.net/problem=377">Problem 377: Sum of digits, experience 13</a>
%H A211072 Tadao Takaoku, <a href="http://www.kurims.kyoto-u.ac.jp/~kyodo/kokyuroku/contents/pdf/1644-10.pdf">A two-level algorithm for generating multiset permutations</a>, RIMS Kokyuroku 1644 (2009), pp. 95-109.
%H A211072 <a href="/index/Rec#order_18">Index entries for linear recurrences with constant coefficients</a>, signature (11,1,-9,-19,-29,-39,-49,-59,-69,-90,-80,-70,-60,-50,-40,-30,-20,-10).
%F A211072 G.f.: x*(9*x^8 + 8*x^7 + 7*x^6 + 6*x^5 + 5*x^4 + 4*x^3 + 3*x^2 + 2*x + 1)/((x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x - 1)*(10*x^9 + 10*x^8 + 10*x^7 + 10*x^6 + 10*x^5 + 10*x^4 + 10*x^3 + 10*x^2 + 10*x - 1)). - _Yurii Ivanov_, Jul 06 2021
%e A211072 2 and 11 are the only numbers without 0's which have digit sum 2, so a(2) = 2 + 11 = 13.
%p A211072 b:= proc(n) option remember; `if`(n=0, [1, 0], add((p->
%p A211072       [p[1], p[2]*10+p[1]*d])(b(n-d)), d=1..min(n, 9)))
%p A211072     end:
%p A211072 a:= n-> b(n)[2]:
%p A211072 seq(a(n), n=0..23);  # _Alois P. Heinz_, Feb 19 2020
%Y A211072 Cf. A007953, A016135, A052382, A130835, A258800.
%K A211072 nonn,base,easy
%O A211072 0,3
%A A211072 _Laurent Desnogues_ and _Charles R Greathouse IV_, Apr 02 2012
%E A211072 a(0)=0 prepended by _Alois P. Heinz_, Feb 19 2020