A027828 -id:A027828 - cp's OEIS frontend

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

Offset: 0

Ilya Gutkovskiy, Oct 05 2016

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))).

			a(0)=0;
a(1)=0+1=1;
a(2)=0+1+2=3;
a(3)=0+1+2+3=6;
...
a(10)=0+1+2+3+4+5+6+7+8+9+11=56;
a(11)=0+1+2+3+4+5+6+7+8+9+11+22=78;
a(12)=0+1+2+3+4+5+6+7+8+9+11+22+33=111, etc.

Eric Weisstein's World of Mathematics, Repdigit
Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,11,-11,0,0,0,0,0,0,0,-10,10).

Cf. A000217, A010785, A027828, A046489.

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]

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.

cp's OEIS Frontend

A277209 Partial sums of repdigit numbers (A010785).

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