This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A328355 #21 Jul 04 2023 14:10:40
%S A328355 0,1,89,7193,576025,46086681,3686971929,294958053913,23596646709785,
%T A328355 1887731755956761,151018540629932569,12081483251621739033,
%U A328355 966518660139556190745,77321492811243031804441,6185719424900070836714009,494857553992010693275990553,39588604319360895672790202905
%N A328355 Let S be any integer in the range 36 <= S <= 44. Sequence has the property that a(n)*S is the sum of all positive integers whose decimal expansion has <= n digits and uses eight distinct nonzero digits d1,d2,d3,d4,d5,d6,d7,d8 such that d1+d2+d3+d4+d5+d6+d7+d8=S.
%C A328355 This sequence is the building block for the calculation of the sums of positive integers whose decimal expansion uses exactly eight distinct, nonzero digits: see the attached pdf documents.
%H A328355 Pierre-Alain Sallard, <a href="/A328355/a328355.pdf">Integers sequences A324348 and A328350 to A328356</a>
%H A328355 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (89, -728, 640).
%F A328355 a(n) = (70*80^n - 79*8^n + 9) / 4977.
%F A328355 a(n) = 81 a(n-1) - 80 a(n-2) + 8^(n-1) for n > 1.
%F A328355 G.f.: x / (1 - 89*x + 728*x^2 - 640*x^3).
%F A328355 a(n) = 89*a(n-1) - 728*a(n-2) + 640*a(n-3) for n > 2.
%F A328355 E.g.f.: (9*exp(x) - 79*exp(8*x) + 70*exp(80*x))/4977. - _Stefano Spezia_, Dec 11 2019
%e A328355 For n=2, the sum of all positive integers whose decimal notation is made of any digit different from 0 and, let's say, 9 with at most n=2 such digits, i.e., the sum 1+2+3+4+5+6+7+8+11+12+13+14+15+16+17+18+21+...+28+31+...+38+41+...+48+51+...+58+61+...+68+71+...+78+81+...+88, is equal to a(2)*(1+2+3+4+5+6+7+8) = 89*36 = 3204.
%e A328355 Similarly, and always with n=2, the sum of all positive integers whose decimal notation is made of any digit different from 0 and, let's say, 8, i.e., the sum 1+2+3+4+5+6+7+9+11+..+17+19+21+...+27+29+31+...+37+39+41+...+47+49+51+...+57+59+61+...+67+69+71+...+77+79+91+...+97+99 is equal to a(2)*(1+2+3+4+5+6+7+9) = 89*37 = 3293.
%t A328355 CoefficientList[Series[x/(1 - 89 x + 728 x^2 - 640 x^3), {x, 0, 16}], x] (* _Michael De Vlieger_, Dec 10 2019 *)
%o A328355 (Python)[(70*80**n-79*8**n+9)//4977 for n in range(20)]
%Y A328355 Cf. A328348, A328350, A328351, A328352, A328353, A328354, A328356.
%K A328355 nonn,base
%O A328355 0,3
%A A328355 _Pierre-Alain Sallard_, Dec 10 2019