A294327
a(n) = ((9*n + 8)*10^n - 8)/9.
Original entry on oeis.org
0, 18, 288, 3888, 48888, 588888, 6888888, 78888888, 888888888, 9888888888, 108888888888, 1188888888888, 12888888888888, 138888888888888, 1488888888888888, 15888888888888888, 168888888888888888, 1788888888888888888, 18888888888888888888, 198888888888888888888
Offset: 0
A294329
a(n) = 8*((9*n + 8)*10^n - 8)/81.
Original entry on oeis.org
0, 16, 256, 3456, 43456, 523456, 6123456, 70123456, 790123456, 8790123456, 96790123456, 1056790123456, 11456790123456, 123456790123456, 1323456790123456, 14123456790123456, 150123456790123456, 1590123456790123456, 16790123456790123456, 176790123456790123456
Offset: 0
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LinearRecurrence[{21,-120,100},{0,16,256},20] (* Harvey P. Dale, Aug 19 2018 *)
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concat(0, Vec(16*x*(1 - 5*x) / ((1 - x)*(1 - 10*x)^2) + O(x^30))) \\ Colin Barker, Oct 28 2017
A104720
Expansion of 1/((1-x)(1-x^2)(1-10x)).
Original entry on oeis.org
1, 11, 112, 1122, 11223, 112233, 1122334, 11223344, 112233445, 1122334455, 11223344556, 112233445566, 1122334455667, 11223344556677, 112233445566778, 1122334455667788, 11223344556677889, 112233445566778899, 1122334455667789000, 11223344556677890010, 112233445566778900111, 1122334455667789001121
Offset: 0
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)
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List([0..25],n->1000*10^n/891+(-1)^n/44-(18*n+47)/324); # Muniru A Asiru, Sep 29 2018
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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
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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 *)
A294344
a(n) = ((-9*n + 82)*10^n - 1)/81.
Original entry on oeis.org
1, 9, 79, 679, 5679, 45679, 345679, 2345679, 12345679, 12345679, -987654321, -20987654321, -320987654321, -4320987654321, -54320987654321, -654320987654321, -7654320987654321, -87654320987654321, -987654320987654321, -10987654320987654321, -120987654320987654321
Offset: 0
Curious multiplications:
9 * 8 = 72;
79 * 8 = 632;
679 * 8 = 5432;
5679 * 8 = 45432;
45679 * 8 = 365432;
345679 * 8 = 2765432;
2345679 * 8 = 18765432.
9 * 9 = 81;
79 * 9 = 711;
679 * 9 = 6111;
5679 * 9 = 51111;
45679 * 9 = 411111;
345679 * 9 = 3111111;
2345679 * 9 = 21111111.
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LinearRecurrence[{21,-120,100},{1,9,79},30] (* Harvey P. Dale, Mar 12 2018 *)
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Vec((1 - 12*x + 10*x^2) / ((1 - x)*(1 - 10*x)^2) + O(x^30)) \\ Colin Barker, Oct 29 2017
Showing 1-4 of 4 results.
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