A089314 Sum of all digits in all even numbers from 0 to 444...4 (with n 4's).

0, 6, 128, 2220, 32112, 421004, 5209896, 62098788, 720987680, 8209876572, 92098765464, 1020987654356, 11209876543248, 122098765432140, 1320987654321032, 14209876543209924, 152098765432098816, 1620987654320987708, 17209876543209876600, 182098765432098765492

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

From Colin Barker, Sep 02 2015: (Start)

a(n) = (9*(9*10^n+28)*n-64*(10^n-1))/81.

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

G.f.: 2*x*(125*x^2-2*x+3) / ((x-1)^2*(10*x-1)^2).

(End)

Example

a(2) = 0+2+4+6+8+1+0+1+2+1+4+..+4+4 = 128.

Mathematica

Table[Sum[Total@ IntegerDigits@ k, {k, 0, FromDigits@ Table[4, {n}], 2}], {n, 0, 8}] (* Michael De Vlieger, Sep 02 2015 *)
LinearRecurrence[{22, -141, 220, -100}, {0, 6, 128, 2220}, 20] (* Harvey P. Dale, Sep 03 2018 *)

Prog

(PARI) concat(0, Vec(2*x*(125*x^2-2*x+3)/((x-1)^2*(10*x-1)^2) + O(x^30))) \\ Colin Barker, Sep 02 2015

Crossrefs

Cf. A089304.

Sequence in context: A223210 A324093 A177756 * A111873 A348796 A012842

Adjacent sequences: A089311 A089312 A089313 * A089315 A089316 A089317

Keyword

nonn,base,easy

Author

Yalcin Aktar, Dec 25 2003

Extensions

More terms from David Wasserman, Sep 09 2005

Status

approved