A089314 - OEIS

%I #21 Sep 03 2018 11:41:18

%S 0,6,128,2220,32112,421004,5209896,62098788,720987680,8209876572,

%T 92098765464,1020987654356,11209876543248,122098765432140,

%U 1320987654321032,14209876543209924,152098765432098816,1620987654320987708,17209876543209876600,182098765432098765492

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

%H Colin Barker, <a href="/A089314/b089314.txt">Table of n, a(n) for n = 0..996</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (22,-141,220,-100).

%F From _Colin Barker_, Sep 02 2015: (Start)

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

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

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

%F (End)

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

%t Table[Sum[Total@ IntegerDigits@ k, {k, 0, FromDigits@ Table[4, {n}], 2}], {n, 0, 8}] (* _Michael De Vlieger_, Sep 02 2015 *)

%t LinearRecurrence[{22,-141,220,-100},{0,6,128,2220},20] (* _Harvey P. Dale_, Sep 03 2018 *)

%o (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

%Y Cf. A089304.

%K nonn,base,easy

%O 0,2

%A _Yalcin Aktar_, Dec 25 2003

%E More terms from _David Wasserman_, Sep 09 2005