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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
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
Sequence in context: A075842 A037535 A065834 * A132926 A094704 A019523
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Mar 20 2005
STATUS
approved

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Last modified March 29 02:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)