A015523 -id:A015523 - cp's OEIS frontend

A180226 a(n) = 4a(n-1) + 10a(n-2), with a(1)=0 and a(2)=1.

0, 1, 4, 26, 144, 836, 4784, 27496, 157824, 906256, 5203264, 29875616, 171535104, 984896576, 5654937344, 32468715136, 186424233984, 1070384087296, 6145778689024, 35286955629056, 202605609406464, 1163291993916416, 6679224069730304, 38349816218085376

Offset: 1

Vladimir Joseph Stephan Orlovsky, Jan 16 2011

Nathaniel Johnston, Table of n, a(n) for n = 1..500
Index entries for linear recurrences with constant coefficients, signature (4, 10).

Cf. A001076, A006190, A007482, A015520, A015521, A015523, A015524, A015525, A015528, A015529, A015530, A015531, A015532, A015533, A015534, A015443, A015447, A030195, A053404, A057087, A083858, A085939, A090017, A091914, A099012, A180222.

I:=[0,1]; [n le 2 select I[n] else 4*Self(n-1) + 10*Self(n-2): n in [1..30]]; // G. C. Greubel, Jan 16 2018

Join[{a=0,b=1},Table[c=4*b+10*a;a=b;b=c,{n,100}]]
LinearRecurrence[{4,10}, {0,1}, 30] (* G. C. Greubel, Jan 16 2018 *)

x='x+O('x^30); concat([0], Vec(x^2/(1-4*x-10*x^2))) \\ G. C. Greubel, Jan 16 2018

a(n) = ((2+sqrt(14))^(n-1) - (2-sqrt(14))^(n-1))/(2*sqrt(14)). - Rolf Pleisch, May 14 2011

G.f.: x^2/(1-4*x-10*x^2).

A152187 a(n) = 3a(n-1) + 5a(n-2), with a(0)=1, a(1)=5.

Original entry on oeis.org

1, 5, 20, 85, 355, 1490, 6245, 26185, 109780, 460265, 1929695, 8090410, 33919705, 142211165, 596232020, 2499751885, 10480415755, 43940006690, 184222098845, 772366329985, 3238209484180, 13576460102465, 56920427728295

Offset: 0

Philippe Deléham, Nov 28 2008

Unsigned version of A152185.
From Johannes W. Meijer, Aug 01 2010: (Start)
The a(n) represent the number of n-move routes of a fairy chess piece starting in a given side square (m = 2, 4, 6 and 8) on a 3 X 3 chessboard. This fairy chess piece behaves like a king on the eight side and corner squares but on the central square the king goes crazy and turns into a red king, see A179596.
The sequence above corresponds to 24 red king vectors, i.e., A[5] vectors, with decimal values 27, 30, 51, 54, 57, 60, 90, 114, 120, 147, 150, 153, 156, 177, 180, 210, 216, 240, 282, 306, 312, 402, 408 and 432. These vectors lead for the corner squares to A015523 and for the central square to A179606.
This sequence belongs to a family of sequences with g.f. (1+2*x)/(1 - 3*x - k*x^2). Red king sequences that are members of this family are A007483 (k=2), A108981 (k=4), A152187 (k=5; this sequence), A154964 (k=6), A179602 (k=7) and A179598 (k=8). We observe that there is no red king sequence for k=3. Other members of this family are A036563 (k=-2), A054486 (k=-1), A084244 (k=0), A108300 (k=1) and A000351 (k=10).
Inverse binomial transform of A015449 (without the first leading 1).
(End)

Index entries for linear recurrences with constant coefficients, signature (3, 5).

Cf. A015523, A072263, A072264, A179606, A197189.

LinearRecurrence[{3,5},{1,5},40] (* Harvey P. Dale, May 03 2013 *)

G.f.: (1+2*x)/(1 - 3*x - 5*x^2).
Lim_{k->infinity} a(n+k)/a(k) = (A072263(n) + A015523(n)*sqrt(29))/2. - Johannes W. Meijer, Aug 01 2010
G.f.: G(0)*(1+2*x)/(2-3*x), where G(k) = 1 + 1/(1 - x*(29*k-9)/(x*(29*k+20) - 6/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, Jun 17 2013

A135030 Generalized Fibonacci numbers: a(n) = 6a(n-1) + 2a(n-2).

Original entry on oeis.org

0, 1, 6, 38, 240, 1516, 9576, 60488, 382080, 2413456, 15244896, 96296288, 608267520, 3842197696, 24269721216, 153302722688, 968355778560, 6116740116736, 38637152257536, 244056393778688, 1541612667187200

Offset: 0

Rolf Pleisch, Feb 10 2008, Feb 14 2008

For n>0, a(n) equals the number of words of length n-1 over {0,1,...,7} in which 0 and 1 avoid runs of odd lengths. - Milan Janjic, Jan 08 2017

Joshua Zucker and Robert Israel, Table of n, a(n) for n = 0..1000 (n=0..51 from Joshua Zucker).
Index entries for linear recurrences with constant coefficients, signature (6, 2).

Cf. A001076, A006190, A007482, A015520, A015521, A015523, A015524, A015525, A015528, A015529, A015530, A015531, A015532, A015533, A015534, A015535, A015536, A015537, A015440, A015441, A015443, A015444, A015445, A015447, A015548, A030195, A053404, A057087, A057088, A083858, A085939, A090017, A091914, A099012, A180222, A180226, A180250.

[n le 2 select n-1 else 6*Self(n-1) + 2*Self(n-2): n in [1..35]]; // Vincenzo Librandi, Sep 18 2016

A:= gfun:-rectoproc({a(0) = 0, a(1) = 1, a(n) = 2*(3*a(n-1) + a(n-2))},a(n),remember):
seq(A(n),n=1..30); # Robert Israel, Sep 16 2014

Join[{a=0,b=1},Table[c=6*b+2*a;a=b;b=c,{n,100}]] (* Vladimir Joseph Stephan Orlovsky, Jan 16 2011 *)
LinearRecurrence[{6,2},{0,1},30] (* or *) CoefficientList[Series[ -(x/(2x^2+6x-1)),{x,0,30}],x] (* Harvey P. Dale, Jun 20 2011 *)

a(n)=([0,1; 2,6]^n*[0;1])[1,1] \\ Charles R Greathouse IV, Oct 03 2016

[lucas_number1(n,6,-2) for n in range(0, 21)] # Zerinvary Lajos, Apr 24 2009

a(0) = 0; a(1) = 1; a(n) = 2*(3*a(n-1) + a(n-2)).
a(n) = 1/(2*sqrt(11))*( (3 + sqrt(11))^n - (3 - sqrt(11))^n ).
G.f.: x/(1 - 6*x - 2*x^2). - Harvey P. Dale, Jun 20 2011
a(n+1) = Sum_{k=0..n} A099097(n,k)*2^k. - Philippe Deléham, Sep 16 2014
E.g.f.: (1/sqrt(11))*exp(3*x)*sinh(sqrt(11)*x). - G. C. Greubel, Sep 17 2016

More terms from Joshua Zucker, Feb 23 2008

A197189 a(n) = 3a(n-1) + 5a(n-2), with a(0)=1, a(1)=2.

Original entry on oeis.org

1, 2, 11, 43, 184, 767, 3221, 13498, 56599, 237287, 994856, 4171003, 17487289, 73316882, 307387091, 1288745683, 5403172504, 22653245927, 94975600301, 398193030538, 1669457093119, 6999336432047, 29345294761736, 123032566445443, 515824173145009, 2162635351662242

Offset: 0

Bruno Berselli, Oct 11 2011

Bruno Berselli, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,5).

Cf. for type of recurrence: A015523, A072263, A072264, A152187, A179606 and also A180140.

[n le 2 select n else 3*Self(n-1)+5*Self(n-2): n in [1..26]];

a = {1, 2}; Do[AppendTo[a, 3 a[[-1]] + 5 a[[-2]]], {24}]; a (* Bruno Berselli, Dec 26 2012 *)

v=vector(26); v[1]=1; v[2]=2; for(i=3, #v, v[i]=3*v[i-1]+5*v[i-2]); v

G.f.: (1-x)/(1-3*x-5*x^2).
a(n) = ((29+sqrt(29))*(3+sqrt(29))^n+(29-sqrt(29))*(3-sqrt(29))^n)/(58*2^n).
a(n) = A015523(n+1)-A015523(n).
G.f.: G(0)*(1-x)/(2-3*x), where G(k)= 1 + 1/(1 - x*(29*k-9)/(x*(29*k+20) - 6/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, Jun 17 2013

A072263 a(n) = 3a(n-1) + 5a(n-2), with a(0)=2, a(1)=3.

Original entry on oeis.org

2, 3, 19, 72, 311, 1293, 5434, 22767, 95471, 400248, 1678099, 7035537, 29497106, 123669003, 518492539, 2173822632, 9113930591, 38210904933, 160202367754, 671661627927, 2815996722551, 11806298307288, 49498878534619, 207528127140297

Offset: 0

Miklos Kristof, Jul 08 2002

Inverse binomial transform of A087130. - Johannes W. Meijer, Aug 01 2010
Pisano period lengths: 1, 3, 4, 6, 4, 12, 3, 12, 12, 12, 120, 12, 12, 3, 4, 24, 288, 12, 72, 12... - R. J. Mathar, Aug 10 2012
This is the Lucas sequence V(3,-5). - Bruno Berselli, Jan 09 2013

			a(5)=5*b(4)+b(6): 1293=5*57+1008.

G. C. Greubel, Table of n, a(n) for n = 0..1000
Wikipedia, Lucas sequence: Specific names.
Index entries for linear recurrences with constant coefficients, signature (3,5).

Cf. A072264, A152187, A197189.

Appears in A179606 and A015523. - Johannes W. Meijer, Aug 01 2010

a:=[2,3];; for n in [3..40] do a[n]:=3*a[n-1]+5*a[n-2]; od; a; # G. C. Greubel, Jan 14 2020

I:=[2,3]; [n le 2 select I[n] else 3*Self(n-1) +5*Self(n-2): n in [1..40]]; // G. C. Greubel, Jan 14 2020

seq(coeff(series((2-3*x)/(1-3*x-5*x^2), x, n+1), x, n), n = 0..40); # G. C. Greubel, Jan 14 2020

LinearRecurrence[{3,5},{2,3},40] (* Harvey P. Dale, Nov 23 2018 *)

my(x='x+O('x^40)); Vec((2-3*x)/(1-3*x-5*x^2)) \\ G. C. Greubel, Jan 14 2020

[lucas_number2(n,3,-5) for n in range(0, 16)] # Zerinvary Lajos, Apr 30 2009

a(n) = 2*A015523(n+1) - 3*A015523(n).
a(n) = ((3 + sqrt(29))/2)^n + ((3 - sqrt(29))/2)^n.
G.f.: (2-3*x)/(1-3*x-5*x^2). - R. J. Mathar, Feb 06 2010
From Johannes W. Meijer, Aug 01 2010: (Start)
Limit_{k -> Infinity} a(n+k)/a(k) = (A072263(n) + A015523(n)*sqrt(29))/2.
Limit_{n -> Infinity} (A072263(n)/A015523(n)) = sqrt(29). (End)
G.f.: G(0), where G(k)= 1 + 1/(1 - x*(29*k-9)/(x*(29*k+20) - 6/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, Jun 17 2013
a(n) = [x^n] ( (1 + 3*x + sqrt(1 + 6*x + 29*x^2))/2 )^n for n >= 1. - Peter Bala, Jun 23 2015
a(n) = 5^((n-1)/2)*( 2*sqrt(5)*Fibonacci(n+1, 3/sqrt(5)) - 3*Fibonacci(n, 3/sqrt(5)) ). - G. C. Greubel, Jan 14 2020

Offset changed and terms added by Johannes W. Meijer, Jul 19 2010

A072264 a(n) = 3a(n-1) + 5a(n-2), with a(0)=1, a(1)=1.

Original entry on oeis.org

1, 1, 8, 29, 127, 526, 2213, 9269, 38872, 162961, 683243, 2864534, 12009817, 50352121, 211105448, 885076949, 3710758087, 15557659006, 65226767453, 273468597389, 1146539629432, 4806961875241, 20153583772883, 84495560694854, 354254600948977, 1485241606321201

Offset: 0

Miklos Kristof, Jul 08 2002

			a(5)=3*a(4)+5*a(3): 127=3*29+5*8=87+40.

G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,5).

Cf. A015523, A072263, A152187, A179606, A197189.

a:=[1,1];; for n in [3..30] do a[n]:=3*a[n-1]+5*a[n-2]; od; a; # G. C. Greubel, Jan 14 2020

[n le 2 select 1 else 3*Self(n-1)+5*Self(n-2): n in [1..26]];  // Bruno Berselli, Oct 11 2011

seq(coeff(series((1-2*x)/(1-3*x-5*x^2), x, n+1), x, n), n = 0..30); # G. C. Greubel, Jan 14 2020

LinearRecurrence[{3,5},{1,1},30] (* Harvey P. Dale, Feb 17 2018 *)

my(x='x+O('x^30)); Vec((1-2*x)/(1-3*x-5*x^2)) \\ G. C. Greubel, Jan 14 2020

def A072264_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1-2*x)/(1-3*x-5*x^2) ).list()
A072264_list(30) # G. C. Greubel, Jan 14 2020

G.f.: (1-2*x)/(1-3*x-5*x^2). - Jaume Oliver Lafont, Mar 06 2009
G.f.: G(0)*(1-2*x)/(2-3*x), where G(k)= 1 + 1/(1 - x*(29*k-9)/(x*(29*k+20) - 6/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, Jun 17 2013
a(n) = 5^((n-1)/2)*( sqrt(5)*Fibonacci(n+1, 3/sqrt(5)) - 2*Fibonacci(n, 3/sqrt(5)) ). - G. C. Greubel, Jan 14 2020

Offset changed and more terms added by Bruno Berselli, Oct 11 2011

A180250 a(n) = 5a(n-1) + 10a(n-2), with a(1)=0 and a(2)=1.

Original entry on oeis.org

0, 1, 5, 35, 225, 1475, 9625, 62875, 410625, 2681875, 17515625, 114396875, 747140625, 4879671875, 31869765625, 208145546875, 1359425390625, 8878582421875, 57987166015625, 378721654296875, 2473479931640625, 16154616201171875, 105507880322265625

Offset: 1

Vladimir Joseph Stephan Orlovsky, Jan 16 2011

Nathaniel Johnston, Table of n, a(n) for n = 1..500
Index entries for linear recurrences with constant coefficients, signature (5,10).

Cf. A001076, A006190, A007482, A015520, A015521, A015523, A015524, A015525, A015528, A015529, A015530, A015531, A015532, A015533, A015534, A015535, A015536, A015537, A015440, A015441, A015443, A015444, A015445, A015447, A030195, A053404, A057087, A057088, A083858, A085939, A090017, A091914, A099012, A180222, A180226.

[n le 2 select n-1 else 5*Self(n-1) +10*Self(n-2): n in [1..30]]; // G. C. Greubel, Jan 16 2018

Join[{a=0,b=1},Table[c=5*b+10*a;a=b;b=c,{n,100}]]
LinearRecurrence[{5,10}, {0,1}, 30] (* G. C. Greubel, Jan 16 2018 *)

a(n)=([0,1;10,5]^(n-1))[1,2] \\ Charles R Greathouse IV, Oct 03 2016

my(x='x+O('x^30)); concat([0], Vec(x^2/(1-5*x-10*x^2))) \\ G. C. Greubel, Jan 16 2018

A180250= BinaryRecurrenceSequence(5,10,0,1)
[A180250(n-1) for n in range(1,41)] # G. C. Greubel, Jul 21 2023

a(n) = ((5+sqrt(65))^(n-1) - (5-sqrt(65))^(n-1))/(2^(n-1)*sqrt(65)). - Rolf Pleisch, May 14 2011
G.f.: x^2/(1-5*x-10*x^2).
a(n) = (i*sqrt(10))^(n-1) * ChebyshevU(n-1, -i*sqrt(5/8)). - G. C. Greubel, Jul 21 2023

A015551 Expansion of x/(1 - 6x - 5x^2).

Original entry on oeis.org

0, 1, 6, 41, 276, 1861, 12546, 84581, 570216, 3844201, 25916286, 174718721, 1177893756, 7940956141, 53535205626, 360916014461, 2433172114896, 16403612761681, 110587537144566, 745543286675801, 5026197405777636

Offset: 0

Olivier Gérard

Let the generator matrix for the ternary Golay G_12 code be [I|B], where the elements of B are taken from the set {0,1,2}. Then a(n)=(B^n)1,2 for instance. - _Paul Barry, Feb 13 2004

Pisano period lengths: 1, 2, 4, 4, 1, 4, 42, 8, 12, 2, 10, 4, 12, 42, 4, 16, 96, 12, 360, 4, ... - R. J. Mathar, Aug 10 2012

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Lucyna Trojnar-Spelina, Iwona Włoch, On Generalized Pell and Pell-Lucas Numbers, Iranian Journal of Science and Technology, Transactions A: Science (2019), 1-7.
Index entries for linear recurrences with constant coefficients, signature (6,5).

Cf. A001076, A006190, A007482, A015520, A015521, A015523, A015524, A015525, A015528, A015529, A015530, A015531, A015532, A015533, A015534, A015535, A015536, A015537, A015440, A015441, A015443, A015444, A015445, A015447, A015548, A030195, A053404, A057087, A057088, A057089, A083858, A085939, A090017, A091914, A099012, A135030, A135032, A180222, A180226, A180250.

I:=[0,1]; [n le 2 select I[n] else 6*Self(n-1)+5*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Nov 14 2011

Join[{a=0,b=1},Table[c=6*b+5*a;a=b;b=c,{n,100}]] (* Vladimir Joseph Stephan Orlovsky, Jan 16 2011 *)
CoefficientList[Series[x/(1-6x-5x^2),{x,0,20}],x] (* or *) LinearRecurrence[ {6,5},{0,1},30] (* Harvey P. Dale, Oct 30 2017 *)

a(n)=([0,1; 5,6]^n*[0;1])[1,1] \\ Charles R Greathouse IV, Oct 03 2016

[lucas_number1(n,6,-5) for n in range(0, 21)] # Zerinvary Lajos, Apr 24 2009

a(n) = 6*a(n-1) + 5*a(n-2).

a(n) = sqrt(14)*(3+sqrt(14))^n/28 - sqrt(14)*(3-sqrt(14))^n/28. - Paul Barry, Feb 13 2004

A189800 a(n) = 6a(n-1) + 8a(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

Vladimir Joseph Stephan Orlovsky, May 24 2011

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (6,8).

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
.A000045,A001045,A006130,A006131,A015440,A015441,A015442,A015443,A015445,A015446
.A000129,A002605,A015518,A063727,A002532,A083099,A015519,A003683,A002534,A083102
.A006190,A007482,A030195,A015521,A015523,A083858,A015524,A015525,A099012,A015528
.A001076,A090017,A015530,A057087,A015531,A085939,A015532,A180222,A015533,A180226
.A052918,A015535,A015536,A015537,A057088,A015540,A015541,A015544,A015545,A180250
.A005668,A135030,A090018,A135032,A015551,A057089,A015552,A189800,A189801,A190005
.A054413,A015555,A015559,A015561,A015562,A015564,A057090,A015565,A015566,A015568
.A041025,A190331,A015574,A190510,A015575,A190560,A015576,A057091,A015577,A190953
.A099371,A015579,A181353,A015580,A015581,A153191,A015583,A015584,A057092,A015585
A041041,A191014,A015588,A190954,A190955,A190956,A015589,A190957,A015591,A057093

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

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 *)

a(n)=([0,1; 8,6]^n*[0;1])[1,1] \\ Charles R Greathouse IV, Oct 03 2016

G.f.: x/(1 - 2*x*(3+4*x)). - Harvey P. Dale, Jul 26 2011

A015541 Expansion of x/(1 - 5x - 7x^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

Olivier Gérard

Pisano period lengths: 1, 3, 8, 6, 8, 24, 6, 6, 24, 24, 5, 24, 12, 6, 8, 12, 16, 24, 120, 24, ... - R. J. Mathar, Aug 10 2012

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (5,7).

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.

[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 *)

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

a(n) = 5*a(n-1) + 7*a(n-2).

cp's OEIS Frontend

A180226 a(n) = 4*a(n-1) + 10*a(n-2), with a(1)=0 and a(2)=1.

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A152187 a(n) = 3*a(n-1) + 5*a(n-2), with a(0)=1, a(1)=5.

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A135030 Generalized Fibonacci numbers: a(n) = 6*a(n-1) + 2*a(n-2).

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A197189 a(n) = 3*a(n-1) + 5*a(n-2), with a(0)=1, a(1)=2.

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A072263 a(n) = 3*a(n-1) + 5*a(n-2), with a(0)=2, a(1)=3.

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A072264 a(n) = 3*a(n-1) + 5*a(n-2), with a(0)=1, a(1)=1.

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A180226 a(n) = 4a(n-1) + 10a(n-2), with a(1)=0 and a(2)=1.

A152187 a(n) = 3a(n-1) + 5a(n-2), with a(0)=1, a(1)=5.

A135030 Generalized Fibonacci numbers: a(n) = 6a(n-1) + 2a(n-2).

A197189 a(n) = 3a(n-1) + 5a(n-2), with a(0)=1, a(1)=2.

A072263 a(n) = 3a(n-1) + 5a(n-2), with a(0)=2, a(1)=3.

A072264 a(n) = 3a(n-1) + 5a(n-2), with a(0)=1, a(1)=1.

A180250 a(n) = 5a(n-1) + 10a(n-2), with a(1)=0 and a(2)=1.

A015551 Expansion of x/(1 - 6x - 5x^2).

A189800 a(n) = 6a(n-1) + 8a(n-2), with a(0)=0, a(1)=1.

A015541 Expansion of x/(1 - 5x - 7x^2).