A089343 Sum of all digits in all even numbers from 0 to 6(10^(k+1)-1)/9 (with (k+1) 6's).

0, 12, 231, 3735, 52239, 672243, 8222247, 97222251, 1122222255, 12722222259, 142222222263, 1572222222267, 17222222222271, 187222222222275, 2022222222222279, 21722222222222283, 232222222222222287, 2472222222222222291, 26222222222222222295

Offset

0,2

Links

Colin Barker, Table of n, a(n) for n = 0..996

Index entries for linear recurrences with constant coefficients, signature (22,-141,220,-100).

Formula

a(k+1) = 3((10^k)(110*3+405k-135)-3(18k+29)+162k+216)/81.

From Colin Barker, Sep 02 2015: (Start)

a(n) = (-7/9*(-1+10^n)+1/2*(8+3*10^n)*n).

a(n) = 22*a(n-1)-141*a(n-2)+220*a(n-3)-100*a(n-4) for n>3.

G.f.: 3*x*(115*x^2-11*x+4) / ((x-1)^2*(10*x-1)^2).

(End)

Example

a(2) = 0+2+4+6+8+1+0+1+2+1+4+..+6+6 = 231.

Mathematica

Table[Sum[Total@ IntegerDigits@ k, {k, 0, FromDigits@ Table[6, {n}], 2}], {n, 0, 8}] (* or *)
Table[(-7/9 (-1 + 10^n) + 1/2 (8 + 3*10^n) n), {n, 0, 18}] (* Michael De Vlieger, Sep 02 2015 *)
LinearRecurrence[{22, -141, 220, -100}, {0, 12, 231, 3735}, 20] (* Vincenzo Librandi, Sep 03 2015 *)

Prog

(PARI) concat(0, Vec(3*x*(115*x^2-11*x+4)/((x-1)^2*(10*x-1)^2) + O(x^30))) \\ Colin Barker, Sep 02 2015
(Magma) [(-7/9*(-1+10^n)+1/2*(8+3*10^n)*n): n in [0..20]]; // Vincenzo Librandi, Sep 03 2015

Crossrefs

Sequence in context: A221657 A089370 A171093 * A303487 A280071 A279610

Adjacent sequences: A089340 A089341 A089342 * A089344 A089345 A089346

Keyword

nonn,base,easy

Author

Yalcin Aktar, Dec 26 2003

Extensions

More terms from Colin Barker, Sep 03 2015

Status

approved