A277209 - OEIS

A277209

Partial sums of repdigit numbers (A010785).

0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 56, 78, 111, 155, 210, 276, 353, 441, 540, 651, 873, 1206, 1650, 2205, 2871, 3648, 4536, 5535, 6646, 8868, 12201, 16645, 22200, 28866, 36643, 45531, 55530, 66641, 88863, 122196, 166640, 222195, 288861, 366638, 455526, 555525, 666636, 888858, 1222191, 1666635, 2222190

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OFFSET

0,3

COMMENTS

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)).

LINKS

Table of n, a(n) for n=0..50.

Eric Weisstein's World of Mathematics, Repdigit

FORMULA

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)).

a(n) = A000217(n) for n < 10.

a(n) = A046489(n-1) for n < 19.

EXAMPLE

a(0)=0;

a(1)=0+1=1;

a(2)=0+1+2=3;

a(3)=0+1+2+3=6;