A015548
Expansion of x/(1 - 5*x - 12*x^2).
Original entry on oeis.org
0, 1, 5, 37, 245, 1669, 11285, 76453, 517685, 3505861, 23741525, 160777957, 1088788085, 7373275909, 49931836565, 338138493733, 2289874507445, 15507034462021, 105013666399445, 711152745541477, 4815927724500725, 32613471569001349
Offset: 0
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[n le 2 select n-1 else 5*Self(n-1) + 12*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Nov 13 2012
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Join[{a=0,b=1},Table[c=5*b+12*a;a=b;b=c,{n,100}]] (* Vladimir Joseph Stephan Orlovsky, Jan 16 2011 *)
LinearRecurrence[{5, 12}, {0, 1}, 30] (* Vincenzo Librandi, Nov 13 2012 *)
CoefficientList[Series[x/(1-5x-12x^2),{x,0,30}],x] (* Harvey P. Dale, May 27 2023 *)
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x='x+O('x^30); concat([0], Vec(x/(1-5*x-12*x^2))) \\ G. C. Greubel, Jan 16 2018
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[lucas_number1(n,5,-12) for n in range(0, 21)] # Zerinvary Lajos, Apr 24 2009
A189800
a(n) = 6*a(n-1) + 8*a(n-2), with a(0)=0, a(1)=1.
Original entry on oeis.org
0, 1, 6, 44, 312, 2224, 15840, 112832, 803712, 5724928, 40779264, 290475008, 2069084160, 14738305024, 104982503424, 747801460736, 5326668791808, 37942424436736, 270267896954880, 1925146777223168, 13713023838978048, 97679317251653632, 695780094221746176
Offset: 0
Sequences of the form a(n) = c*a(n-1) + d*a(n-2), with a(0)=0, a(1)=1:
c/d...1.......2.......3.......4.......5.......6.......7.......8.......9......10
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I:=[0,1]; [n le 2 select I[n] else 6*Self(n-1)+8*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Nov 14 2011
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LinearRecurrence[{6, 8}, {0, 1}, 50]
CoefficientList[Series[-(x/(-1+6 x+8 x^2)),{x,0,50}],x] (* Harvey P. Dale, Jul 26 2011 *)
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a(n)=([0,1; 8,6]^n*[0;1])[1,1] \\ Charles R Greathouse IV, Oct 03 2016
A287815
Number of octonary sequences of length n such that no two consecutive terms have distance 7.
Original entry on oeis.org
1, 8, 62, 482, 3746, 29114, 226274, 1758602, 13667858, 106226618, 825593474, 6416514026, 49869159026, 387583197338, 3012297335522, 23411580532682, 181954847741906, 1414153417389434, 10990803008177474, 85420541561578922, 663888608980117298, 5159743512230294618
Offset: 0
For n=2 the a(2) = 64 - 2 = 62 sequences contain every combination except these two: 07,70.
Cf.
A040000,
A003945,
A083318,
A078057,
A003946,
A126358,
A003946,
A055099,
A003947,
A015448,
A126473.
A287804-
A287819.
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LinearRecurrence[{7, 6}, {1, 8}, 40]
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def a(n):
if n in [0, 1]:
return [1, 8][n]
return 7*a(n-1)+6*a(n-2)
Showing 1-3 of 3 results.