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
KEYWORD
nonn,base,easy
AUTHOR
Yalcin Aktar, Dec 26 2003
EXTENSIONS
More terms from Colin Barker, Sep 03 2015
STATUS
approved