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A104720 Expansion of 1/((1-x)(1-x^2)(1-10x)). 2
1, 11, 112, 1122, 11223, 112233, 1122334, 11223344, 112233445, 1122334455, 11223344556, 112233445566, 1122334455667, 11223344556677, 112233445566778, 1122334455667788, 11223344556677889, 112233445566778899, 1122334455667789000, 11223344556677890010, 112233445566778900111, 1122334455667789001121 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Partial sums of A056830(n+1).

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..999

Index entries for linear recurrences with constant coefficients, signature (11,-9,-11,10).

FORMULA

a(n) = 1000*10^n/891 + (-1)^n/44 - (18n+47)/324.

a(n) = floor((2*10^(n+3) - 99n)/1782). - Hieronymus Fischer, Dec 05 2006

a(n) = 10*a(n-1) + (2*n + 3 + (-1)^n)/4, a(0)=1, a(1)=11. - Vincenzo Librandi, Mar 22 2011

EXAMPLE

From Seiichi Manyama, Sep 29 2018: (Start)

   1                  * 8 + 0  = 8;

   11                 * 8 + 1  = 89;

   112                * 8 + 1  = 897;

   1122               * 8 + 2  = 8978;

   11223              * 8 + 2  = 89786;

   112233             * 8 + 3  = 897867;

   1122334            * 8 + 3  = 8978675;

   11223344           * 8 + 4  = 89786756;

   112233445          * 8 + 4  = 897867564;

   1122334455         * 8 + 5  = 8978675645;

   11223344556        * 8 + 5  = 89786756453;

   112233445566       * 8 + 6  = 897867564534;

   1122334455667      * 8 + 6  = 8978675645342;

   11223344556677     * 8 + 7  = 89786756453423;

   112233445566778    * 8 + 7  = 897767564534231;

   1122334455667788   * 8 + 8  = 8978675645342312;

   11223344556677889  * 8 + 8  = 89786756453423120;

   112233445566778899 * 8 + 9  = 897867564534231201.

   1                  * 9 + 1  = 10;

   11                 * 9 + 2  = 101;

   112                * 9 + 2  = 1010;

   1122               * 9 + 3  = 10101;

   11223              * 9 + 3  = 101010;

   112233             * 9 + 4  = 1010101;

   1122334            * 9 + 4  = 10101010;

   11223344           * 9 + 5  = 101010101;

   112233445          * 9 + 5  = 1010101010;

   1122334455         * 9 + 6  = 10101010101;

   11223344556        * 9 + 6  = 101010101010;

   112233445566       * 9 + 7  = 1010101010101;

   1122334455667      * 9 + 7  = 10101010101010;

   11223344556677     * 9 + 8  = 101010101010101;

   112233445566778    * 9 + 8  = 1010101010101010;

   1122334455667788   * 9 + 9  = 10101010101010101;

   11223344556677889  * 9 + 9  = 101010101010101010;

   112233445566778899 * 9 + 10 = 1010101010101010101. (End)

MAPLE

seq(coeff(series(((1-x)*(1-x^2)*(1-10*x))^(-1), x, n+1), x, n), n = 0 .. 25); # Muniru A Asiru, Sep 29 2018

MATHEMATICA

a[n_]:=1000*10^n/891 + (-1)^n/44 - (18*n + 47)/324 ; Array[a, 50, 0] (* or *)

a[n_]:=Floor[(2*10^(n + 3) - 99*n)/1782]; Array[a, 50, 0] (* Stefano Spezia, Sep 01 2018 *)

LinearRecurrence[{11, -9, -11, 10}, {1, 11, 112, 1122}, 30] (* Harvey P. Dale, Jun 20 2021 *)

PROG

(GAP) List([0..25], n->1000*10^n/891+(-1)^n/44-(18*n+47)/324); # Muniru A Asiru, Sep 29 2018

CROSSREFS

Cf. A056830, A294328, A294344.

Sequence in context: A075842 A037535 A065834 * A132926 A094704 A019523

Adjacent sequences:  A104717 A104718 A104719 * A104721 A104722 A104723

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Mar 20 2005

STATUS

approved

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Last modified November 27 12:51 EST 2021. Contains 349394 sequences. (Running on oeis4.)