A015541
Expansion of x/(1 - 5*x - 7*x^2).
Original entry on oeis.org
0, 1, 5, 32, 195, 1199, 7360, 45193, 277485, 1703776, 10461275, 64232807, 394392960, 2421594449, 14868722965, 91294775968, 560554940595, 3441838134751, 21133075257920, 129758243232857, 796722742969725, 4891921417478624, 30036666288181195
Offset: 0
Cf.
A001076,
A006190,
A007482,
A015520,
A015521,
A015523,
A015524,
A015525,
A015528,
A015529,
A015530,
A015531,
A015532,
A015533,
A015534,
A015535,
A015536,
A015537,
A015443,
A015447,
A030195,
A053404,
A057087,
A057088,
A083858,
A085939,
A090017,
A091914,
A099012,
A180222,
A180226.
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[n le 2 select n-1 else 5*Self(n-1) + 7*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Nov 13 2012
-
Join[{a=0,b=1},Table[c=5*b+7*a;a=b;b=c,{n,100}]] (* Vladimir Joseph Stephan Orlovsky, Jan 16 2011 *)
LinearRecurrence[{5, 7}, {0, 1}, 30] (* Vincenzo Librandi, Nov 13 2012 *)
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x='x+O('x^30); concat([0], Vec(x/(1-5*x-7*x^2))) \\ G. C. Greubel, Jan 24 2018
-
[lucas_number1(n,5,-7) for n in range(0, 21)] # Zerinvary Lajos, Apr 24 2009
A015544
Lucas sequence U(5,-8): a(n+1) = 5*a(n) + 8*a(n-1), a(0)=0, a(1)=1.
Original entry on oeis.org
0, 1, 5, 33, 205, 1289, 8085, 50737, 318365, 1997721, 12535525, 78659393, 493581165, 3097180969, 19434554165, 121950218577, 765227526205, 4801739379641, 30130517107845, 189066500576353, 1186376639744525, 7444415203333449, 46713089134623445
Offset: 0
Cf.
A001076,
A006190,
A007482,
A015520,
A015521,
A015523,
A015524,
A015525,
A015528,
A015529,
A015530,
A015531,
A015532,
A015533,
A015534,
A015535,
A015536,
A015537,
A015441,
A015443,
A015447,
A030195,
A053404,
A057087,
A057088,
A083858,
A085939,
A090017,
A091914,
A099012,
A180222,
A180226,
A015555 (binomial transform).
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[n le 2 select n-1 else 5*Self(n-1) + 8*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Nov 13 2012
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a[n_]:=(MatrixPower[{{1,2},{1,-6}},n].{{1},{1}})[[2,1]]; Table[Abs[a[n]],{n,-1,40}] (* Vladimir Joseph Stephan Orlovsky, Feb 19 2010 *)
LinearRecurrence[{5, 8}, {0, 1}, 30] (* Vincenzo Librandi, Nov 13 2012 *)
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A015544(n)=imag((2+quadgen(57))^n) \\ M. F. Hasler, Mar 06 2009
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x='x+O('x^30); concat([0], Vec(x/(1 - 5*x - 8*x^2))) \\ G. C. Greubel, Jan 01 2018
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[lucas_number1(n,5,-8) for n in range(0, 21)] # Zerinvary Lajos, Apr 24 2009
A106567
a(n) = 5*a(n-1) + 4*a(n-2), with a(0) = 4, a(1) = 4.
Original entry on oeis.org
0, 4, 20, 116, 660, 3764, 21460, 122356, 697620, 3977524, 22678100, 129300596, 737215380, 4203279284, 23965257940, 136639406836, 779058065940, 4441847957044, 25325472048980, 144394752073076, 823275648561300, 4693957251098804, 26762888849739220
Offset: 0
-
I:=[0,4]; [n le 2 select I[n] else 5*Self(n-1) +4*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Mar 22 2018
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CoefficientList[Series[4*x/(1-5*x-4*x^2), {x, 0, 30}], x] (* Vincenzo Librandi, Mar 22 2018 *)
LinearRecurrence[{5,4},{0,4},30] (* Harvey P. Dale, Jan 19 2025 *)
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a(n) = (([0,4; 1,5]^n)*[0,1]~)[1]; \\ Michel Marcus, Mar 22 2018
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def A106567_list(prec):
P. = PowerSeriesRing(ZZ, prec)
return P( 4*x/(1-5*x-4*x^2) ).list()
A106567_list(30) # G. C. Greubel, Sep 06 2021
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