A089350 Sum of all digits in all even numbers from 0 to 8(10^(k+1)-1)/9 (with (k+1) 8's).

0, 20, 360, 5520, 75080, 950640, 11506200, 135061760, 1550617320, 17506172880, 195061728440, 2150617284000, 23506172839560, 255061728395120, 2750617283950680, 29506172839506240, 315061728395061800, 3350617283950617360, 35506172839506172920

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) = 4((10^k)(110*4+405k-135)-4(18k+29)+162k+216)/81.

From Colin Barker, Sep 02 2015: (Start)

a(n) = (2*(-20*(-1+10^n)+9*(20+9*10^n)*n))/81.

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

G.f.: 20*x*(21*x^2-4*x+1) / ((x-1)^2*(10*x-1)^2).

(End)

Example

a(2) = 0+2+4+6+8+1+0+1+2+1+4+..+8+8 = 360.

Mathematica

Table[Sum[Total@ IntegerDigits@ k, {k, 0, FromDigits@ Table[8, {n}], 2}], {n, 0, 8}] (* or *)
Table[(2 (-20 (-1 + 10^n) + 9 (20 + 9*10^n) n))/81, {n, 0, 18}] (* Michael De Vlieger, Sep 02 2015 *)
LinearRecurrence[{22, -141, 220, -100}, {0, 20, 360, 5520}, 20] (* Vincenzo Librandi, Sep 03 2015 *)

Prog

(PARI) concat(0, Vec(20*x*(21*x^2-4*x+1) / ((x-1)^2*(10*x-1)^2) + O(x^30))) \\ Colin Barker, Sep 02 2015
(Magma) [(2*(-20*(-1+10^n)+9*(20+9*10^n)*n))/81: n in [0..20]]; // Vincenzo Librandi, Sep 03 2015

Crossrefs

Sequence in context: A285393 A156455 A358365 * A323961 A004292 A053508

Adjacent sequences: A089347 A089348 A089349 * A089351 A089352 A089353

Keyword

nonn,base,easy

Author

Yalcin Aktar, Dec 26 2003

Extensions

More terms from Colin Barker, Sep 03 2015

Status

approved