A155600
a(n) = 9^n-2^n+1^n.
Original entry on oeis.org
1, 8, 78, 722, 6546, 59018, 531378, 4782842, 43046466, 387419978, 3486783378, 31381057562, 282429532386, 2541865820138, 22876792438578, 205891132061882, 1853020188786306, 16677181699535498, 150094635296736978
Offset: 0
Cf.
A074501,
A020515,
A155588,
A155590,
A155592,
A155593,
A155594,
A155596,
A155597,
A155598,
A155599.
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Table[9^n - 2^n + 1, {n, 0, 25}] (* or *)
LinearRecurrence[{12, -29, 18}, {1, 8, 78}, 26] (* Paolo Xausa, Jul 19 2024 *)
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a(n)=9^n-2^n+1 \\ Charles R Greathouse IV, Sep 24 2015
A016133
Expansion of 1/((1-2*x)*(1-9*x)).
Original entry on oeis.org
1, 11, 103, 935, 8431, 75911, 683263, 6149495, 55345711, 498111911, 4483008223, 40347076055, 363123688591, 3268113205511, 29413018865983, 264717169826615, 2382454528505071, 21442090756676711, 192978816810352543, 1736809351293697175, 15631284161644323151
Offset: 0
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Kalika Prasad, Munesh Kumari, Rabiranjan Mohanta, and Hrishikesh Mahato, The sequence of higher order Mersenne numbers and associated binomial transforms, arXiv:2307.08073 [math.NT], 2023.
- Index entries for linear recurrences with constant coefficients, signature (11,-18).
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[+9^(n+1)/7 -2^(n+1)/7 : n in [0..20]]; // Vincenzo Librandi, Aug 14 2011
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CoefficientList[Series[1/((1-2x)(1-9x)),{x,0,30}],x] (* or *) LinearRecurrence[ {11,-18},{1,11},30] (* Harvey P. Dale, Apr 19 2020 *)
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Vec(1/((1-2*x)*(1-9*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 23 2012
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[lucas_number1(n,11,18) for n in range(1, 20)] # Zerinvary Lajos, Apr 27 2009
A248216
a(n) = 6^n - 2^n.
Original entry on oeis.org
0, 4, 32, 208, 1280, 7744, 46592, 279808, 1679360, 10077184, 60465152, 362795008, 2176778240, 13060685824, 78364147712, 470184951808, 2821109841920, 16926659313664, 101559956406272, 609359739486208, 3656158439014400, 21936950638280704
Offset: 0
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[6^n-2^n: n in [0..25]];
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Table[6^n - 2^n, {n, 0, 25}] (* or *) CoefficientList[Series[4x/((1-2x)(1-6x)), {x, 0, 30}], x]
LinearRecurrence[{8,-12},{0,4},30] (* Harvey P. Dale, Dec 21 2019 *)
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[2^n*(3^n -1) for n in (0..25)] # G. C. Greubel, Feb 09 2021
Showing 1-3 of 3 results.