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A277209 Partial sums of repdigit numbers (A010785). 0
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 (list; graph; refs; listen; history; text; internal format)
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 * A089717 A050760 A075057

Adjacent sequences:  A277206 A277207 A277208 * A277210 A277211 A277212

KEYWORD

nonn,base,easy

AUTHOR

Ilya Gutkovskiy, Oct 05 2016

STATUS

approved

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Last modified October 18 07:58 EDT 2018. Contains 316307 sequences. (Running on oeis4.)