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 A220094 #27 Jul 08 2017 17:26:36 %S A220094 45,4455,404595,36446355,3280467195,295244704755,26572047342795, %T A220094 2391484476085155,215233604784766395,19371024448062897555, %U A220094 1743392200482566077995,156905298044843094701955,14121476824048587852317595,1270932914164487290670858355 %N A220094 Sum of the n-digit base-ten numbers whose digits are nonzero. %C A220094 For n >= 1, a(n) is the sum of the numbers with n digits in base ten whose digits belong to the set {1,2,3,4,5,6,7,8,9}. %C A220094 If E_n is the set of the numbers with n digits in base ten whose digits belong to {1,2,3,4,5,6,7,8,9}, then card(E_n) = 9^n (see A001019). %D A220094 A. Ducos, Eléments fondamentaux de Math Sup, Ellipses, 1994, exercice 9, p. 126. %H A220094 Bernard Schott and Raymond Cordier, <a href="http://www.les-mathematiques.net/phorum/read.php?17,796056,796562#msg-796562">Question Comtet 16</a> (French mathematical forum les-mathematiques.net) %H A220094 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (99,-810). %F A220094 a(n) = 5*9^(n-1)*(10^n-1). %F A220094 Generalization to base b with n-digit numbers whose digits belong to {1,2,...,b-1}: a_b(n) = (b/2)*(b-1)^(n-1)*(b^n-1). %F A220094 From _Colin Barker_, Jan 04 2013: (Start) %F A220094 a(n) = 99*a(n-1) - 810*a(n-2). %F A220094 G.f.: 45*x/((9*x-1)*(90*x-1)). (End) %e A220094 For n=2, in base ten, a(2) = 11+12+...+19+21+...+89+91+...+98+99 = 4455. %p A220094 := n->5*9^(n-1)*(10^n-1); %t A220094 Table[5*9^(n - 1)*(10^n - 1), {n, 20}] (* _T. D. Noe_, Dec 31 2012 *) %o A220094 (PARI) a(n)=5*9^(n-1)*(10^n-1) \\ _Charles R Greathouse IV_, Jul 06 2017 %Y A220094 Cf. A192107, A192370. %K A220094 nonn,base,easy %O A220094 1,1 %A A220094 _Bernard Schott_, Dec 04 2012