A211072 - OEIS

%I #42 Jul 06 2021 15:59:35

%S 0,1,13,147,1625,17891,196833,2165227,23817625,261994131,2881935943,

%T 31701296375,348714262017,3835856884757,42194425724149,

%U 464138682802857,5105525508895321,56160780576260645,617768586100819485,6795454444489330049,74749998860563784655

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

%C Different from A016135.

%H 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 Project Euler, <a href="http://projecteuler.net/problem=377">Problem 377: Sum of digits, experience 13</a>

%H 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 <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 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 2 and 11 are the only numbers without 0's which have digit sum 2, so a(2) = 2 + 11 = 13.

%p b:= proc(n) option remember; `if`(n=0, [1, 0], add((p->

%p       [p[1], p[2]*10+p[1]*d])(b(n-d)), d=1..min(n, 9)))

%p     end:

%p a:= n-> b(n)[2]:

%p seq(a(n), n=0..23);  # _Alois P. Heinz_, Feb 19 2020

%Y Cf. A007953, A016135, A052382, A130835, A258800.

%K nonn,base,easy

%O 0,3

%A _Laurent Desnogues_ and _Charles R Greathouse IV_, Apr 02 2012

%E a(0)=0 prepended by _Alois P. Heinz_, Feb 19 2020