cp's OEIS Frontend

A277209 Partial sums of repdigit numbers (A010785).

%I A277209 #14 Mar 08 2025 02:29:36
%S A277209 0,1,3,6,10,15,21,28,36,45,56,78,111,155,210,276,353,441,540,651,873,
%T A277209 1206,1650,2205,2871,3648,4536,5535,6646,8868,12201,16645,22200,28866,
%U A277209 36643,45531,55530,66641,88863,122196,166640,222195,288861,366638,455526,555525,666636,888858,1222191,1666635,2222190
%N A277209 Partial sums of repdigit numbers (A010785).
%C A277209 More generally, the ordinary generating function for the partial sums of numbers that are repdigits in base k (for k > 1) is (Sum_{m = 1..(k-1)} m*x^m)/((1 - x)*(1 - x^(k-1))*(1 - k*x^(k-1))).
%H A277209 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Repdigit.html">Repdigit</a>
%H A277209 <a href="/index/Rec#order_19">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,0,0,11,-11,0,0,0,0,0,0,0,-10,10).
%F A277209 G.f.: x*(1 + 2*x + 3*x^2 + 4*x^3 + 5*x^4 + 6*x^5 + 7*x^6 + 8*x^7 + 9*x^8)/((1 - x)*(1 - x^9)*(1 - 10*x^9)).
%F A277209 a(n) = A000217(n) for n < 10.
%F A277209 a(n) = A046489(n-1) for n < 19.
%e A277209 a(0)=0;
%e A277209 a(1)=0+1=1;
%e A277209 a(2)=0+1+2=3;
%e A277209 a(3)=0+1+2+3=6;
%e A277209 ...
%e A277209 a(10)=0+1+2+3+4+5+6+7+8+9+11=56;
%e A277209 a(11)=0+1+2+3+4+5+6+7+8+9+11+22=78;
%e A277209 a(12)=0+1+2+3+4+5+6+7+8+9+11+22+33=111, etc.
%t A277209 CoefficientList[Series[x (1 + 2 x + 3 x^2 + 4 x^3 + 5 x^4 + 6 x^5 + 7 x^6 + 8 x^7 + 9 x^8)/((1 - x) (1 - 10 x^9) (1 - x^9)), {x, 0, 50}], x]
%Y A277209 Cf. A000217, A010785, A027828, A046489.
%K A277209 nonn,base,easy
%O A277209 0,3
%A A277209 _Ilya Gutkovskiy_, Oct 05 2016