A001077 -id:A001077 - cp's OEIS frontend

A163063 Lucas(3n+2) = Fibonacci(3n+1) + Fibonacci(3n+3).

3, 11, 47, 199, 843, 3571, 15127, 64079, 271443, 1149851, 4870847, 20633239, 87403803, 370248451, 1568397607, 6643838879, 28143753123, 119218851371, 505019158607, 2139295485799, 9062201101803, 38388099893011

Offset: 0

Al Hakanson (hawkuu(AT)gmail.com), Jul 20 2009

Binomial transform of A163062. Second binomial transform of A163114. Inverse binomial transform of A098648 without initial 1.

Nathaniel Johnston, Table of n, a(n) for n = 0..400
Index entries for linear recurrences with constant coefficients, signature (4,1).

Cf. A000032, A000045, A163062, A163114, A098648, A001077 (L(3*n)/L(2)), A048876 (L(3*n+1)).

Z:=PolynomialRing(Integers()); N:=NumberField(x^2-5); S:=[ ((3+r)*(2+r)^n+(3-r)*(2-r)^n)/2: n in [0..21] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jul 21 2009

[Lucas(3*n+2): n in [0..30]]; // Vincenzo Librandi, Apr 18 2011

with(combinat):A163063:=proc(n)return fibonacci(3*n+1) + fibonacci(3*n+3): end:seq(A163063(n), n=0..21); # Nathaniel Johnston, Apr 18 2011

Table[Fibonacci[3n + 1] + Fibonacci[3n + 3], {n, 0, 21}] (* Alonso del Arte, Nov 29 2010 *)
LinearRecurrence[{4,1},{3,11},30] (* Harvey P. Dale, Apr 14 2021 *)

Vec((3-x)/(1-4*x-x^2) + O(x^100)) \\ Altug Alkan, Dec 10 2015

a(n) = 4*a(n-1)+a(n-2) for n > 1; a(0) = 3, a(1) = 11.
G.f.: (3-x)/(1-4*x-x^2).
a(n) = A033887(n) + A014445(n+1).
a(n) = ((3+sqrt(5))*(2+sqrt(5))^n+(3-sqrt(5))*(2-sqrt(5))^n)/2.
a(n) = A000032(3*n+2), n>=0, (Lucas trisection). - Wolfdieter Lang, Mar 09 2011.
a(n) = 5*F(n)*F(n+1)*L(n+1) + L(n+2)*(-1)^n with F(n)=A000045(n) and L(n)=A000032(n). - J. M. Bergot, Dec 10 2015

Edited and extended beyond a(5) by Klaus Brockhaus, Jul 21 2009

A042934 Numerators of continued fraction convergents to sqrt(999).

Original entry on oeis.org

31, 32, 63, 95, 158, 885, 5468, 6353, 37233, 80819, 441328, 522147, 3574210, 18393197, 21967407, 40360604, 62328011, 102688615, 6429022141, 6531710756, 12960732897, 19492443653, 32453176550

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 205377230, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).

Cf. A042935 (denominators).

Analog for other sqrt(m): A001333 (m=2), A002531 (m=3), A001077 (m=5), A041006 (m=6), A041008 (m=7), A041010 (m=8), A005667 (m=10), A041014 (m=11), ..., A042936 (m=1000).

Numerator[Convergents[Sqrt[999], 30]] (* Vincenzo Librandi, Dec 10 2013 *)

A42934=contfracpnqn(c=contfrac(sqrt(999)), #c)[1,][^-1] \\ Discard possibly incorrect last element. NB: a(n) = A42934[n+1]! For more terms, use:
A042934(n)={n<#A42934 || A42934_upto(n+10); A42934[n+1]}
{A42934_upto(N,A=Vec(A42934,N))=for(n=#A42934+1,N, A[n]=205377230*A[n-18]-A[n-36]); A42934=A} \\ M. F. Hasler, Nov 01 2019

a(n) = 205377230*a(n-18) - a(n-36). - Wesley Ivan Hurt, May 28 2021

A048878 Generalized Pellian with second term of 9.

Original entry on oeis.org

1, 9, 37, 157, 665, 2817, 11933, 50549, 214129, 907065, 3842389, 16276621, 68948873, 292072113, 1237237325, 5241021413, 22201322977, 94046313321, 398386576261, 1687592618365, 7148757049721, 30282620817249, 128279240318717, 543399582092117, 2301877568687185

Offset: 0

Barry E. Williams

			a(n) = 4a(n-1) + a(n-2); a(0)=1, a(1)=9.

Harry J. Smith, Table of n, a(n) for n = 0..1584
Tanya Khovanova, Recursive Sequences.
Index entries for linear recurrences with constant coefficients, signature (4,1).

Cf. A000045, A015448, A001077, A001076, A033887.

with(combinat): a:=n->5*fibonacci(n-1,4)+fibonacci(n,4): seq(a(n), n=1..16); # Zerinvary Lajos, Apr 04 2008

LinearRecurrence[{4,1},{1,9},31] (* or *) CoefficientList[ Series[ (1+5x)/(1-4x-x^2),{x,0,30}],x] (* Harvey P. Dale, Jul 12 2011 *)

{ default(realprecision, 2000); for (n=0, 2000, a=round(((7+sqrt(5))*(2+sqrt(5))^n - (7-sqrt(5))*(2-sqrt(5))^n )/10*sqrt(5)); if (a > 10^(10^3 - 6), break); write("b048878.txt", n, " ", a); ); } \\ Harry J. Smith, May 31 2009

a(n) = ( (7+sqrt(5))(2+sqrt(5))^n - (7-sqrt(5))(2-sqrt(5))^n )/2*sqrt(5).
G.f.: (1+5*x)/(1-4*x-x^2). - Philippe Deléham, Nov 03 2008
a(n) = F(3*n+3) + F(3*n-2); F = A000045. - Yomna Bakr and Greg Dresden, May 25 2024

A162963 a(n) = 5*a(n-2) for n > 2; a(1) = 2, a(2) = 5.

Original entry on oeis.org

2, 5, 10, 25, 50, 125, 250, 625, 1250, 3125, 6250, 15625, 31250, 78125, 156250, 390625, 781250, 1953125, 3906250, 9765625, 19531250, 48828125, 97656250, 244140625, 488281250, 1220703125, 2441406250, 6103515625, 12207031250

Offset: 1

Klaus Brockhaus, Jul 19 2009

Binomial transform is A162770, second binomial transform is A001077 without initial 1, third binomial transform is A162771, fourth binomial transform is A162772, fifth binomial transform is A162773.

Index entries for linear recurrences with constant coefficients, signature (0,5).

Cf. A000351 (powers of 5), A026383, A001077, A162770, A162771, A162772, A162773.

[ n le 2 select 3*n-1 else 5*Self(n-2): n in [1..29] ];

a(n) = (3-(-1)^n)*5^(1/4*(2*n-1+(-1)^n))/2.
G.f.: x*(2+5*x)/(1-5*x^2).
a(n) = A026383(n) for n >= 1.

A164581 a(n) = 5*a(n - 1) + a(n - 2), with a(0)=1, a(1)=2.

Original entry on oeis.org

1, 2, 11, 57, 296, 1537, 7981, 41442, 215191, 1117397, 5802176, 30128277, 156443561, 812346082, 4218173971, 21903215937, 113734253656, 590574484217, 3066606674741, 15923607857922, 82684645964351, 429346837679677, 2229418834362736, 11576441009493357

Offset: 0

Vincenzo Librandi, Aug 17 2009

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (5,1).

Cf. A000032, A001077, A052924, A078343, A179237, A180148, A329723.

[ n le 2 select (n) else 5*Self(n-1)+Self(n-2): n in [1..25] ]; // Vincenzo Librandi, Sep 12 2013

LinearRecurrence[{5, 1}, {1, 2}, 40] (* or *) Rest[CoefficientList[Series [x (1 - 3 x) / (1 - 5 x - x^2), {x, 0, 40}], x]] (* Harvey P. Dale, May 02 2011 *)

Vec((1-3*x)/(1-5*x-x^2) + O(x^40)) \\ Colin Barker, Oct 13 2015

a(n) = 5*a(n-1)+a(n-2) = A052918(n)-3*A052918(n-1).
G.f.: (1-3*x)/(1-5*x-x^2).
a(n) = A052918(n) + A015449(n). - R. J. Mathar, Jul 06 2012
a(n) = (2^(-1-n)*((5-sqrt(29))^n*(1+sqrt(29))+(-1+sqrt(29))*(5+sqrt(29))^n))/sqrt(29). - Colin Barker, Oct 13 2015
a(n) = Sum_{k=0..n-2} A168561(n-2,k)*5^k + 2 * Sum_{k=0..n-1} A168561(n-1,k)*5^k, n>0. - R. J. Mathar, Feb 14 2024
a(n) = A052918(n) -3*A052918(n-1). - R. J. Mathar, Feb 14 2024
From Peter Bala, Jul 08 2025: (Start)
The following series telescope:
Sum_{n >= 1} 1/(a(n) - 7*(-1)^n/a(n)) = 3/10, since 1/(a(n) - 7*(-1)^n/a(n)) = b(n) - b(n+1), where b(n) = (1/5) * (a(n) + a(n-1)) / (a(n)*a(n-1)).
Sum_{n >= 1} (-1)^(n+1)/(a(n) - 7*(-1)^n/a(n)) = 1/10, since 1/(a(n) - 7*(-1)^n/a(n)) = c(n) + c(n+1), where c(n) = (1/5) * (a(n) - a(n-1)) / (a(n)*a(n-1)). (End)

A110528 a(n+3) = 3a(n+2) + 5a(n+1) + a(n), a(0) = 1, a(1) = 10, a(2) = 37.

Original entry on oeis.org

1, 10, 37, 162, 681, 2890, 12237, 51842, 219601, 930250, 3940597, 16692642, 70711161, 299537290, 1268860317, 5374978562, 22768774561, 96450076810, 408569081797, 1730726404002, 7331474697801, 31056625195210

Offset: 0

Creighton Dement, Jul 24 2005

Compare with A110526, A110527.

G. C. Greubel, Table of n, a(n) for n = 0..1000
Robert Munafo, Sequences Related to Floretions
Index entries for linear recurrences with constant coefficients, signature (3,5,1).

Cf. A110526, A110527.

seriestolist(series(-(1+7*x+2*x^2)/((1+x)*(x^2+4*x-1)), x=0,25)); -or- Floretion Algebra Multiplication Program, FAMP Code: 2tesseq[(- 'i + 'j - i' + j' - 'kk' - 'ik' - 'jk' - 'ki' - 'kj')(+ .5'i + .5i' + .5'jj' + .5'kk')]

LinearRecurrence[{3,5,1},{1,10,37},30] (* Harvey P. Dale, Apr 21 2016 *)

x='x+O('x^50); Vec(-(1+7*x+2*x^2)/((1+x)*(x^2+4*x-1))) \\ G. C. Greubel, Aug 30 2017

G.f.: -(1 + 7*x + 2*x^2)/((1 + x)*(x^2 + 4*x - 1)).

a(n) = A001077(n+1) - (-1)^n. - Ehren Metcalfe, Nov 18 2017

A162771 a(n) = ((2+sqrt(5))(3+sqrt(5))^n + (2-sqrt(5))(3-sqrt(5))^n)/2.

Original entry on oeis.org

2, 11, 58, 304, 1592, 8336, 43648, 228544, 1196672, 6265856, 32808448, 171787264, 899489792, 4709789696, 24660779008, 129125515264, 676109975552, 3540157792256, 18536506851328, 97058409938944, 508204432228352

Offset: 0

Al Hakanson (hawkuu(AT)gmail.com), Jul 13 2009

nonn

Binomial transform of A001077 without initial 1. Third binomial transform of A162963. Inverse binomial transform of A162772.

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (6,-4).

Cf. A001077, A002878, A162963, A162772.

Z:=PolynomialRing(Integers()); N:=NumberField(x^2-5); S:=[ ((2+r)*(3+r)^n+(2-r)*(3-r)^n)/2: n in [0..20] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jul 19 2009

LinearRecurrence[{6,-4},{2,11},30] (* Harvey P. Dale, Aug 15 2013 *)
CoefficientList[Series[(2 - x) / (1 - 6 x + 4 x^2), {x, 0, 30}], x] (* Vincenzo Librandi, Aug 16 2013 *)

a(n) = 6*a(n-1) - 4*a(n-2) for n > 1; a(0) = 2, a(1) = 11. [corrected by Harvey P. Dale, Aug 15 2013]
G.f.: (2-x)/(1-6*x+4*x^2).
a(n) = 2^(n-1) * A002878(n+1). - Diego Rattaggi, Jun 16 2020
a(n) = Sum_{k>=1} binomial(k+n-1,n) * A000032(k) / 2^(k+1). - Diego Rattaggi, Aug 02 2020

Edited and extended beyond a(5) by Klaus Brockhaus, Jul 19 2009

A191347 Array read by antidiagonals: ((floor(sqrt(n)) + sqrt(n))^k + (floor(sqrt(n)) - sqrt(n))^k)/2 for columns k >= 0 and rows n >= 0.

Original entry on oeis.org

1, 0, 1, 0, 1, 1, 0, 2, 1, 1, 0, 4, 3, 1, 1, 0, 8, 7, 4, 2, 1, 0, 16, 17, 10, 8, 2, 1, 0, 32, 41, 28, 32, 9, 2, 1, 0, 64, 99, 76, 128, 38, 10, 2, 1, 0, 128, 239, 208, 512, 161, 44, 11, 2, 1, 0, 256, 577, 568, 2048, 682, 196, 50, 12, 3, 1

Offset: 0

Charles L. Hohn, May 31 2011

			1, 0,  0,   0,    0,    0,     0,      0,       0,        0,        0, ...
1, 1,  2,   4,    8,   16,    32,     64,     128,      256,      512, ...
1, 1,  3,   7,   17,   41,    99,    239,     577,     1393,     3363, ...
1, 1,  4,  10,   28,   76,   208,    568,    1552,     4240,    11584, ...
1, 2,  8,  32,  128,  512,  2048,   8192,   32768,   131072,   524288, ...
1, 2,  9,  38,  161,  682,  2889,  12238,   51841,   219602,   930249, ...
1, 2, 10,  44,  196,  872,  3880,  17264,   76816,   341792,  1520800, ...
1, 2, 11,  50,  233, 1082,  5027,  23354,  108497,   504050,  2341691, ...
1, 2, 12,  56,  272, 1312,  6336,  30592,  147712,   713216,  3443712, ...
1, 3, 18, 108,  648, 3888, 23328, 139968,  839808,  5038848, 30233088, ...
1, 3, 19, 117,  721, 4443, 27379, 168717, 1039681,  6406803, 39480499, ...
1, 3, 20, 126,  796, 5028, 31760, 200616, 1267216,  8004528, 50561600, ...
1, 3, 21, 135,  873, 5643, 36477, 235791, 1524177,  9852435, 63687141, ...
1, 3, 22, 144,  952, 6288, 41536, 274368, 1812352, 11971584, 79078912, ...
1, 3, 23, 153, 1033, 6963, 46943, 316473, 2133553, 14383683, 96969863, ...
...

Row 1 is A000007, row 2 is A011782, row 3 is A001333, row 4 is A026150, row 5 is A081294, row 6 is A001077, row 7 is A084059, row 8 is A108851, row 9 is A084128, row 10 is A081341, row 11 is A005667, row 13 is A141041.
Row 3*2 is A002203, row 4*2 is A080040, row 5*2 is A155543, row 6*2 is A014448, row 8*2 is A080042, row 9*2 is A170931, row 11*2 is A085447.
Cf. A191348 which uses ceiling() in place of floor().

T(n, k) = if (n==0, k==0, my(x=sqrtint(n)); sum(i=0, (k+1)\2, binomial(k, 2*i)*x^(k-2*i)*n^i));
matrix(9,9, n, k, T(n-1,k-1)) \\ Michel Marcus, Aug 22 2019

T(n, k) = if (k==0, 1, if (k==1, sqrtint(n), T(n,k-2)*(n-T(n,1)^2) + T(n,k-1)*T(n,1)*2));
matrix(9, 9, n, k, T(n-1, k-1)) \\ Charles L. Hohn, Aug 22 2019

For each row n>=0 let T(n,0)=1 and T(n,1)=floor(sqrt(n)), then for each column k>=2: T(n,k)=T(n,k-2)*(n-T(n,1)^2) + T(n,k-1)*T(n,1)*2. - Charles L. Hohn, Aug 22 2019

T(n, k) = Sum_{i=0..floor((k+1)/2)} binomial(k, 2*i)*floor(sqrt(n))^(k-2*i)*n^i for n > 0, with T(0, 0) = 1 and T(0, k) = 0 for k > 0. - Michel Marcus, Aug 23 2019

A193735 Mirror of the triangle A193734.

Original entry on oeis.org

1, 2, 1, 8, 6, 1, 32, 32, 10, 1, 128, 160, 72, 14, 1, 512, 768, 448, 128, 18, 1, 2048, 3584, 2560, 960, 200, 22, 1, 8192, 16384, 13824, 6400, 1760, 288, 26, 1, 32768, 73728, 71680, 39424, 13440, 2912, 392, 30, 1, 131072, 327680, 360448, 229376, 93184, 25088, 4480, 512, 34, 1

Offset: 0

Clark Kimberling, Aug 04 2011

A193735 is obtained by reversing the rows of the triangle A193734.

Triangle T(n,k), read by rows, given by (2,2,0,0,0,0,0,0,0,...) DELTA (1,0,0,0,0,0,0,0,...) where DELTA is the operator defined in A084938. - Philippe Deléham, Oct 05 2011

			First six rows:
    1;
    2,   1;
    8,   6,   1;
   32,  32,  10,   1;
  128, 160,  72,  14,  1;
  512, 768, 448, 128, 18, 1;

G. C. Greubel, Rows n = 0..50 of the triangle, flattened

Cf. A084938, A193722, A193734.

Cf. A001075, A001077, A005053, A081294, A133494.

function T(n, k) // T = A193735
  if k lt 0 or k gt n then return 0;
  elif n lt 2 then return n-k+1;
  else return 4*T(n-1, k) + T(n-1, k-1);
  end if;
end function;
[T(n, k): k in [0..n], n in [0..12]]; // G. C. Greubel, Nov 19 2023

(* First program *)
z = 8; a = 2; b = 1; c = 1; d = 2;
p[n_, x_] := (a*x + b)^n ; q[n_, x_] := (c*x + d)^n
t[n_, k_] := Coefficient[p[n, x], x^k]; t[n_, 0] := p[n, x] /. x -> 0;
w[n_, x_] := Sum[t[n, k]*q[n + 1 - k, x], {k, 0, n}]; w[-1, x_] := 1
g[n_] := CoefficientList[w[n, x], {x}]
TableForm[Table[Reverse[g[n]], {n, -1, z}]]
Flatten[Table[Reverse[g[n]], {n, -1, z}]] (* A193734 *)
TableForm[Table[g[n], {n, -1, z}]]
Flatten[Table[g[n], {n, -1, z}]]      (* A193735 *)
(* Second program *)
T[n_, k_]:= T[n, k]= If[k<0 || k>n, 0, If[n<2, n-k+1, 4*T[n-1, k] + T[n -1, k-1]]];
Table[T[n,k], {n,0,12}, {k,0,n}]//Flatten (* G. C. Greubel, Nov 19 2023 *)

def T(n, k): # T = A193735
    if (k<0 or k>n): return 0
    elif (n<2): return n-k+1
    else: return 4*T(n-1, k) + T(n-1, k-1)
flatten([[T(n, k) for k in range(n+1)] for n in range(13)]) # G. C. Greubel, Nov 19 2023

T(n,k) = A193734(n,n-k).
T(n,k) = T(n-1,k-1) + 4*T(n-1,k) with T(0,0)=T(1,1)=1 and T(1,0)=2. - Philippe Deléham, Oct 05 2011
G.f.: (1-2*x)/(1-4*x-x*y). - R. J. Mathar, Aug 11 2015
From G. C. Greubel, Nov 19 2023: (Start)
T(n, 0) = A081294(n).
Sum_{k=0..n} T(n, k) = A005053(n).
Sum_{k=0..n} (-1)^k * T(n, k) = A133494(n).
Sum_{k=0..floor(n/2)} T(n-k, k) = A001077(n).
Sum_{k=0..floor(n/2)} (-1)^k * T(n-k, k) = A001075(n). (End)

A207608 Triangle of coefficients of polynomials u(n,x) jointly generated with A207609; see the Formula section.

Original entry on oeis.org

1, 2, 3, 3, 4, 11, 3, 5, 26, 20, 3, 6, 50, 74, 29, 3, 7, 85, 204, 149, 38, 3, 8, 133, 469, 547, 251, 47, 3, 9, 196, 952, 1618, 1160, 380, 56, 3, 10, 276, 1764, 4110, 4234, 2124, 536, 65, 3, 11, 375, 3048, 9318, 13036, 9262, 3520, 719, 74, 3, 12, 495, 4983

Offset: 1

Clark Kimberling, Feb 19 2012

As triangle T(n,k) with 0<=k<=n and with zeros omitted, it is (2, -1/2, 1/2, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (0, 3/2, -1/2, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938. - Philippe Deléham, Mar 03 2012

			First five rows:
  1;
  2;
  3,  3;
  4, 11,  3;
  5, 26, 20,  3;
Triangle (2, -1/2, 1/2, 0, 0, 0, 0, ...) DELTA (0, 3/2, -1/2, 0, 0, 0, 0, ...) begins:
  1;
  2,   0;
  3,   3,   0;
  4,  11,   3,   0;
  5,  26,  20,   3,   0;
  6,  50,  74,  29,   3,   0;
  7,  85, 204, 149,  38,   3,   0;
  ... - _Philippe Deléham_, Mar 03 2012

Cf. A207609.

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + v[n - 1, x]
v[n_, x_] := 2 x*u[n - 1, x] + (x + 1) v[n - 1, x]
Table[Factor[u[n, x]], {n, 1, z}]
Table[Factor[v[n, x]], {n, 1, z}]
cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
TableForm[cu]
Flatten[%]    (* A207608 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]  (* A207609 *)

from sympy import Poly
from sympy.abc import x
def u(n, x): return 1 if n==1 else u(n - 1, x) + v(n - 1, x)
def v(n, x): return 1 if n==1 else 2*x*u(n - 1, x) + (x + 1)*v(n - 1, x)
def a(n): return Poly(u(n, x), x).all_coeffs()[::-1]
for n in range(1, 13): print(a(n)) # Indranil Ghosh, May 28 2017

u(n,x) = u(n-1,x) + v(n-1,x),
v(n,x) = 2x*u(n-1,x) + (x+1)v(n-1,x),
where u(1,x)=1, v(1,x)=1.
From Philippe Deléham, Mar 03 2012: (Start)
As triangle T(n,k), 0 <= k <= n:
T(n,k) = 2*T(n-1,k) + T(n-1,k-1) - T(n-1,k) + T(n-2,k-1) with T(0,0) = 1, T(1,0) = 2, T(1,1) = 0 and T(n,k) = 0 if k < 0 or if k > n.
G.f.: (1-y*x)/(1 - (2+y)*x - (y-1)*x^2).
Sum_{k=0..n} T(n,k)*x^k = A000027(n+1), A025192(n), A001077(n), A180038(n) for x = 0, 1, 2, 3 respectively. (End)

cp's OEIS Frontend

A163063 Lucas(3n+2) = Fibonacci(3n+1) + Fibonacci(3n+3).

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A042934 Numerators of continued fraction convergents to sqrt(999).

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A048878 Generalized Pellian with second term of 9.

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A162963 a(n) = 5*a(n-2) for n > 2; a(1) = 2, a(2) = 5.

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A164581 a(n) = 5*a(n - 1) + a(n - 2), with a(0)=1, a(1)=2.

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A110528 a(n+3) = 3*a(n+2) + 5*a(n+1) + a(n), a(0) = 1, a(1) = 10, a(2) = 37.

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A162771 a(n) = ((2+sqrt(5))*(3+sqrt(5))^n + (2-sqrt(5))*(3-sqrt(5))^n)/2.

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A110528 a(n+3) = 3a(n+2) + 5a(n+1) + a(n), a(0) = 1, a(1) = 10, a(2) = 37.

A162771 a(n) = ((2+sqrt(5))(3+sqrt(5))^n + (2-sqrt(5))(3-sqrt(5))^n)/2.