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

0,3

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;
...
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.

Mathematica

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]

Crossrefs

Cf. A000217, A010785, A027828, A046489.

Sequence in context: A025715 A165145 A046489 * A361751 A089717 A050760

Adjacent sequences: A277206 A277207 A277208 * A277210 A277211 A277212

Keyword

nonn,base,easy

Author

Ilya Gutkovskiy, Oct 05 2016

Status

approved