A157014 -id:A157014 - cp's OEIS frontend

A238379 Expansion of (1 - x)/(1 - 36*x + x^2).

1, 35, 1259, 45289, 1629145, 58603931, 2108112371, 75833441425, 2727895778929, 98128414600019, 3529895029821755, 126978092658983161, 4567681440693572041, 164309553772309610315, 5910576254362452399299, 212616435603275976764449

Offset: 0

Bruno Berselli, Feb 25 2014

First bisection of A041611.

Bruno Berselli, Table of n, a(n) for n = 0..100
Tanya Khovanova, Recursive Sequences
Index entries for linear recurrences with constant coefficients, signature (36,-1).

Cf. similar sequences with g.f. (1-x)/(1-k*x+x^2): A122367 (k=3), A079935 (k=4), A004253 (k=5), A001653 (k=6), A049685 (k=7), A070997 (k=8), A070998 (k=9), A138288 (k=10), A078922 (k=11), A077417 (k=12), A085260 (k=13), A001570 (k=14), A160682 (k=15), A157456 (k=16), A161595 (k=17). From 18 to 38, even k only, except k=27 and k=31: A007805 (k=18), A075839 (k=20), A157014 (k=22), A159664 (k=24), A153111 (k=26), A097835 (k=27), A159668 (k=28), A157877 (k=30), A111216 (k=31), A159674 (k=32), A077420 (k=34), this sequence (k=36), A097315 (k=38).

[n le 2 select 35^(n-1) else 36*Self(n-1)-Self(n-2): n in [1..20]];

R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1 - x)/(1 - 36*x + x^2))); // Marius A. Burtea, Jan 14 2020

CoefficientList[Series[(1 - x)/(1 - 36 x + x^2), {x, 0, 20}], x] (* or *) LinearRecurrence[{36, -1}, {1, 35}, 20]

a(n)=([0,1; -1,36]^n*[1;35])[1,1] \\ Charles R Greathouse IV, May 10 2016

m = 20; L. = PowerSeriesRing(ZZ, m); f = (1-x)/(1-36*x+x^2)
print(f.coefficients())

G.f.: (1 - x)/(1 - 36*x + x^2).
a(n) = a(-n-1) = 36*a(n-1) - a(n-2).
a(n) = ((19-sqrt(323))/38)*(1+(18+sqrt(323))^(2*n+1))/(18+sqrt(323))^n.
a(n+1) - a(n) = 34*A144128(n+1).
323*a(n+1)^2 - ((a(n+2)-a(n))/2)^2 = 34.
Sum_{n>0} 1/(a(n) - 1/a(n)) = 1/34.
See also Tanya Khovanova in Links field:
a(n) = 35*a(n-1) + 34*Sum_{i=0..n-2} a(i).
a(n+2)*a(n) - a(n+1)^2 = 36-2 = 34 = 34*1,
a(n+3)*a(n) - a(n+1)*a(n+2) = 36*(36-2) = 1224 = 34*36.
Generalizing:
a(n+4)*a(n) - a(n+1)*a(n+3) = 44030 = 34*1295,
a(n+5)*a(n) - a(n+1)*a(n+4) = 1583856 = 34*46584,
a(n+6)*a(n) - a(n+1)*a(n+5) = 56974786 = 34*1675729, etc.,
where 1, 36, 1295, 46584, 1675729, ... is the sequence A144128, which is the second bisection of A041611.
a(n)^2 - 36*a(n)*a(n+1) + a(n+1)^2 + 34 = 0 (see comments by Colin Barker in similar sequences).

A157877 Expansion of (1-x)x/(x^2-30x+1).

Original entry on oeis.org

1, 29, 869, 26041, 780361, 23384789, 700763309, 20999514481, 629284671121, 18857540619149, 565096933903349, 16934050476481321, 507456417360536281, 15206758470339607109, 455695297692827676989, 13655652172314490702561, 409213869871741893399841

Offset: 1

Paul Weisenhorn, Mar 08 2009

This sequence is part of a solution of a more general problem involving 2 equations, three sequences a(n), b(n), c(n) and a constant A:
    A    * c(n)+1 = a(n)^2,
   (A+1) * c(n)+1 = b(n)^2, for details see comment in A157014.
A157877 is the a(n) sequence for A=7.
Positive values of x (or y) satisfying x^2 - 30xy + y^2 + 28 = 0. - Colin Barker, Feb 23 2014

Vincenzo Librandi, Table of n, a(n) for n = 1..200
Index entries for linear recurrences with constant coefficients, signature (30,-1).

Cf. A157879, A157877, A157878.

Cf. similar sequences listed in A238379.

I:=[1,29,869]; [n le 3 select I[n] else 30*Self(n-1)-Self(n-2): n in [1..20]]; // Vincenzo Librandi, Feb 25 2014

LinearRecurrence[{30,-1},{1,29},30] (* Harvey P. Dale, Dec 14 2011 *)
CoefficientList[Series[(1 - x)/(x^2 - 30 x + 1), {x, 0, 40}], x] (* Vincenzo Librandi, Feb 25 2014 *)

Vec((1-x)*x/(x^2-30*x+1)+O(x^99)) \\ Charles R Greathouse IV, Sep 25 2012

G.f.: (1-x)*x/(x^2-30*x+1).
a(1)=1, a(2)=29; for n>2, a(n) = 30*a(n-1)-a(n-2).
7*A157879(n)+1 = a(n)^2.
8*A157879(n)+1 = A157878(n)^2.
a(n) = (1/8)*(4-sqrt(14))*(1+(15+4*sqrt(14))^(2*n-1))/(15+4*sqrt(14))^(n-1). - Bruno Berselli, Feb 25 2014
From Andrea Pinos, Oct 05 2022: (Start)
a(n) = ceiling((C^n)/(C+1)), where C = 15 + 4*sqrt(14) = sqrt(225) + sqrt(224).
Limit_{n->oo} a(n+1)/a(n) = C. (End)

Edited by Alois P. Heinz, Sep 09 2011

A157879 Expansion of 120x^2 / (-x^3+899x^2-899*x+1).

Original entry on oeis.org

0, 120, 107880, 96876240, 86994755760, 78121193796360, 70152745034375640, 62997086919675528480, 56571313901123590199520, 50800976886122064323640600, 45619220672423712639039059400, 40966009362859607827792751700720, 36787430788627255405645251988187280

Offset: 1

Paul Weisenhorn, Mar 08 2009

This sequence is part of a solution of a more general problem involving 2 equations, three sequences a(n), b(n), c(n) and a constant A:
    A    * c(n)+1 = a(n)^2,
   (A+1) * c(n)+1 = b(n)^2, for details see comment in A157014.
A157879 is the c(n) sequence for A=7.

Colin Barker, Table of n, a(n) for n = 1..300
Index entries for linear recurrences with constant coefficients, signature (899,-899,1).

7*A157879(n)+1 = A157877(n)^2.
8*A157879(n)+1 = A157878(n)^2.
Cf. A245031.

CoefficientList[Series[120x^2/(-x^3+899x^2-899x+1),{x,0,30}],x] (* or *) LinearRecurrence[{899,-899,1},{0,0,120},30] (* Harvey P. Dale, Jan 14 2014 *)

concat(0, Vec(120*x^2/(-x^3+899*x^2-899*x+1)+O(x^20))) \\ Charles R Greathouse IV, Sep 25 2012

a(n) = round(-((449+120*sqrt(14))^(-n)*(-1+(449+120*sqrt(14))^n)*(15+4*sqrt(14)+(-15+4*sqrt(14))*(449+120*sqrt(14))^n))/224) \\ Colin Barker, Jul 25 2016

G.f.: 120*x^2/(-x^3+899*x^2-899*x+1).
c(1) = 0, c(2) = 120, c(3) = 899*c(2), c(n) = 899 * (c(n-1)-c(n-2)) + c(n-3) for n>3.
a(n) = -((449+120*sqrt(14))^(-n)*(-1+(449+120*sqrt(14))^n)*(15+4*sqrt(14)+(-15+4*sqrt(14))*(449+120*sqrt(14))^n))/224. - Colin Barker, Jul 25 2016

Edited by Alois P. Heinz, Sep 09 2011

A153111 Solutions of the Pell-like equation 1 + 6AA = 7BB, with A, B integers.

Original entry on oeis.org

1, 25, 649, 16849, 437425, 11356201, 294823801, 7654062625, 198710804449, 5158826853049, 133930787374825, 3477041644892401, 90269151979827601, 2343520909830625225, 60841274503616428249, 1579529616184196509249, 41006928746285492812225

Offset: 1

Ctibor O. Zizka, Dec 18 2008

B is of the form B(i) = 26*B(i-1) - B(i-2) for B(0) = 1, B(1) = 25 (this sequence).
A is of the form A(i) = 26*A(i-1) - A(i-2) for A(0) = 1, A(1) = 27.
In general a Pell-like equation of the form 1 + X*A*A = (X + 1)*B*B has the solution A(i) = (4*X + 2)*A(i-1) - A(i-2), for A(0) = 1 and A(1) = (4*X + 3), and B(i) = (4*X + 2)*B(i-1) - B(i-2) for B(0) = 1 and B(1) = (4*X + 1).
Examples in the OEIS:
  X = 1 gives A002315 for A(i) and A001653 for B(i);
  X = 2 gives A054320 for A(i) and A072256 for B(i);
  X = 3 gives A028230 for A(i) and A001570 for B(i);
  X = 4 gives A049629 for A(i) and A007805 for B(i);
  X = 5 gives A133283 for A(i) and A157014 for B(i);
  X = 6 gives A157461 for A(i) and this sequence for B(i).
Positive values of x (or y) satisfying x^2 - 26*x*y + y^2 + 24 = 0. - Colin Barker, Feb 20 2014

Vincenzo Librandi, Table of n, a(n) for n = 1..200
Luigi Cimmino, Algebraic relations for recursive sequences, arXiv:math/0510417 [math.NT], 2005-2008.
Jeroen Demeyer, Diophantine sets of polynomials over number fields, arXiv:0807.1970 [math.NT], 2008.
Franz Lemmermeyer, Conics - a Poor Man's Elliptic Curves, arXiv:math/0311306 [math.NT], 2003.
Index entries for linear recurrences with constant coefficients, signature (26,-1).

Cf. A002315, A001653, A054320, A072256, A001078, A028230, A001570, A049629, A007805, A133283, A140480.

Cf. similar sequences listed in A238379.

I:=[1,25]; [n le 2 select I[n] else 26*Self(n-1)-Self(n-2): n in [1..20]]; // Vincenzo Librandi, Feb 22 2014

CoefficientList[Series[(1 - x)/(x^2 - 26 x + 1), {x, 0, 40}], x] (* Vincenzo Librandi, Feb 22 2014 *)
LinearRecurrence[{26, -1}, {1, 25}, 20] (* Jean-François Alcover, Jan 07 2019 *)

Vec(-x*(x-1)/(x^2-26*x+1) + O(x^100)) \\ Colin Barker, Feb 20 2014

a(n) = 26*a(n-1) - a(n-2). - Colin Barker, Feb 20 2014
G.f.: -x*(x - 1) / (x^2 - 26*x + 1). - Colin Barker, Feb 20 2014
a(n) = (1/14)*(7 - sqrt(42))*(1 + (13 + 2*sqrt(42))^(2*n - 1))/(13 + 2*sqrt(42))^(n - 1). - Bruno Berselli, Feb 25 2014
E.g.f.: (1/7)*(7*cosh(2*sqrt(42)*x) - sqrt(42)*sinh(2*sqrt(42)*x))*exp(13*x) - 1. - Franck Maminirina Ramaharo, Jan 07 2019

More terms from Philippe Deléham, Sep 19 2009; corrected by N. J. A. Sloane, Sep 20 2009

Additional term from Colin Barker, Feb 20 2014

A133283 Numbers k such that 30*k^2 + 6 is a square.

Original entry on oeis.org

1, 23, 505, 11087, 243409, 5343911, 117322633, 2575754015, 56549265697, 1241508091319, 27256628743321, 598404324261743, 13137638505015025, 288429642786068807, 6332314502788498729, 139022489418560903231, 3052162452705551372353, 67008551470103569288535

Offset: 1

Richard Choulet, Oct 16 2007

From Klaus Purath, Apr 19 2025: (Start)
Nonnegative solutions to the Diophantine equation 5*a(n)^2 - 6*b(n)^2 = -1. The corresponding b(n) are A157014(n). Note that (a(n+1)^2 - a(n)*a(n+2))/4 = 6 and (b(n)*b(n+2) - b(n+1)^2)/4 = 5.
(a(n) + b(n))/2 = (a(n+1) - b(n+1))/2 = A077421(n-1) = Lucas U(22,1). Also a(n)*b(n+1) - a(n+1)*b(n) = -2.
a(n+1) = (t(i+2*n+1) - t(i))/(t(i+n+1) - t(i+n)) as long as t(i+n+1) - t(i+n) != 0 for integer i and n >= 0 where (t) is a sequence satisfying t(i+3) = 23*t(i+2) - 23*t(i+1) + t(i) or t(i+2) = 22*t(i+1) - t(i), regardless of the initial values and including this sequence itself. (End)

Colin Barker, Table of n, a(n) for n = 1..700
Index entries for linear recurrences with constant coefficients, signature (22,-1).

Cf. A221874.

a:=[1,23];; for n in [3..20] do a[n]:=22*a[n-1]-a[n-2]; od; a; # G. C. Greubel, Jan 13 2020

I:=[1,23]; [n le 2 select I[n] else 22*Self(n-1) - Self(n-2): n in [1..20]]; // G. C. Greubel, Jan 13 2020

a[1]:=1: a[2]:=23: for n to 14 do a[n+2]:=22*a[n+1]-a[n] end do: seq(a[n],n= 1..16); # Emeric Deutsch, Oct 24 2007

Table[n /. {ToRules[Reduce[n > 0 && k >= 0 && 30*n^2+6 == k^2, n, Integers] /. C[1] -> c]} // Simplify, {c, 1, 20}] // Flatten // Union (* Jean-François Alcover, Dec 19 2013 *)
Rest@ CoefficientList[Series[x(1+x)/(1-22x+x^2), {x,0,20}], x] (* Michael De Vlieger, Jul 14 2016 *)
LinearRecurrence[{22,-1},{1,23},20] (* Harvey P. Dale, Sep 22 2017 *)
Table[ChebyshevU[n-1, 11] + ChebyshevU[n-2, 11], {n, 20}] (* G. C. Greubel, Jan 13 2020 *)

Vec(x*(1+x)/(1-22*x+x^2) + O(x^20)) \\ Colin Barker, Jul 14 2016

vector(20, n, polchebyshev(n-1,2,11) + polchebyshev(n-2,2,11) ) \\ G. C. Greubel, Jan 13 2020

[chebyshev_U(n-1,11) + chebyshev_U(n-2,11) for n in (1..20)] # G. C. Greubel, Jan 13 2020

a(n+2) = 22*a(n+1) - a(n); a(n+1) = 11*a(n) + 2*sqrt(30*a(n)^2 + 6).
a(n) = (sqrt(30)/10 - 1/2)*(11 + 2*sqrt(30))^n - (sqrt(30)/10 + 1/2) * (11 - 2*sqrt(30))^n. - Emeric Deutsch, Oct 24 2007
G.f.: x*(1+x)/(1-22*x+x^2). - R. J. Mathar, Nov 14 2007
a(n) = A077421(n) + A077421(n-1). - R. J. Mathar, Feb 19 2016
a(n) = Chebyshev(n-1, 11) + Chebyshev(n-2, 11). - G. C. Greubel, Jan 13 2020

More terms from Emeric Deutsch, Oct 24 2007

A157459 Expansion of 72x^2 / (1 - 323x + 323*x^2 - x^3).

Original entry on oeis.org

0, 72, 23256, 7488432, 2411251920, 776415629880, 250003421569512, 80500325329753056, 25920854752758914592, 8346434730063040745640, 2687526062225546361181560, 865375045601895865259716752, 278648077157748243067267612656, 89723815469749332371794911558552

Offset: 1

Paul Weisenhorn, Mar 01 2009

This sequence is part of a solution of a more general problem involving two equations, three sequences a(n), b(n), c(n) and a constant A:
    A    * c(n) + 1 = a(n)^2,
   (A+1) * c(n) + 1 = b(n)^2; for details see comment in A157014.
A157459 is the c(n) sequence for A=4.

Colin Barker, Table of n, a(n) for n = 1..250
Index entries for linear recurrences with constant coefficients, signature (323,-323,1).

Cf. A007805, A049629, A157014, A157459, A201003, A298271.

LinearRecurrence[{323,-323,1},{0,72,23256},20] (* Harvey P. Dale, Feb 28 2021 *)

concat(0, Vec(72*x^2/(1-323*x+323*x^2-x^3)+O(x^20))) \\ Charles R Greathouse IV, Sep 26 2012

a(n) = -round((161+72*sqrt(5))^(-n)*(-1+(161+72*sqrt(5))^n)*(9+4*sqrt(5)+(-9+4*sqrt(5))*(161+72*sqrt(5))^n))/80 \\ Colin Barker, Jul 25 2016

4*a(n) + 1 = A007805(n-1)^2.
5*a(n) + 1 = A049629(n-1)^2.
G.f.: 72*x^2/(1 - 323*x + 323*x^2 - x^3).
c(1) = 0, c(2) = 72, c(3) = 323*c(2), c(n) = 323*(c(n-1) - c(n-2)) + c(n-3) for n>3.
a(n) = -((161+72*sqrt(5))^(-n)*(-1+(161+72*sqrt(5))^n)*(9+4*sqrt(5)+(-9+4*sqrt(5))*(161+72*sqrt(5))^n))/80. - Colin Barker, Jul 25 2016
a(n) = 72*A298271(n-1). - Greg Dresden, Dec 02 2021
a(n) = 2*A201003(n-1). - Amiram Eldar, Dec 01 2024

Edited by Alois P. Heinz, Sep 09 2011

A157461 Expansion of x(x+1) / (x^2-26x+1).

Original entry on oeis.org

1, 27, 701, 18199, 472473, 12266099, 318446101, 8267332527, 214632199601, 5572169857099, 144661784084973, 3755634216352199, 97501827841072201, 2531291889651525027, 65716087303098578501, 1706086977990911515999, 44292545340460600837473

Offset: 1

Paul Weisenhorn, Mar 01 2009

This sequence is part of a solution of a more general problem involving two equations, three sequences a(n), b(n), c(n) and a constant A:
    A    * c(n)+1 = a(n)^2,
   (A+1) * c(n)+1 = b(n)^2, for details see comment in A157014.
A157461 is the b(n) sequence for A=6.
Numbers k such that 42*k^2 + 7 is a square. - Klaus Purath, Jun 12 2021

Colin Barker, Table of n, a(n) for n = 1..700
Index entries for linear recurrences with constant coefficients, signature (26,-1).

6*A157874(n)+1 = A153111(n)^2.

7*A157874(n)+1 = A157461(n)^2.

Vec(x*(x+1)/(x^2-26*x+1)+O(x^20)) \\ Charles R Greathouse IV, Sep 26 2012

a(n) = round((13+2*sqrt(42))^(-n)*(-6-sqrt(42)+(-6+sqrt(42))*(13+2*sqrt(42))^(2*n))/12) \\ Colin Barker, Jul 25 2016

G.f.: x*(x+1) / (x^2-26*x+1).
a(1) = 1, a(2) = 27, a(n) = 26*a(n-1)-a(n-2) for n>2.
a(n) = (13+2*sqrt(42))^(-n)*(-6-sqrt(42)+(-6+sqrt(42))*(13+2*sqrt(42))^(2*n))/12. - Colin Barker, Jul 25 2016
a(n+1) = (a(n)^2 - 28)/a(n-1), n > 1. - Klaus Purath, Jun 12 2021

Edited by Alois P. Heinz, Sep 09 2011

A157878 Expansion of x(1+x)/(x^2-30x+1).

Original entry on oeis.org

1, 31, 929, 27839, 834241, 24999391, 749147489, 22449425279, 672733610881, 20159558901151, 604114033423649, 18103261443808319, 542493729280825921, 16256708616980969311, 487158764780148253409, 14598506234787466632959, 437468028278843850735361

Offset: 1

Paul Weisenhorn, Mar 08 2009

This sequence is part of a solution of a more general problem involving 2 equations, three sequences a(n), b(n), c(n) and a constant A:
    A    * c(n)+1 = a(n)^2,
   (A+1) * c(n)+1 = b(n)^2, for details see comment in A157014.
this is the b(n) sequence for A=7.

Robert Israel, Table of n, a(n) for n = 1..610
Index entries for linear recurrences with constant coefficients, signature (30,-1).

7*A157879(n)+1 = A157877(n)^2.

8*A157879(n)+1 = A157878(n)^2.

f:= gfun:-rectoproc({a(1) = 1, a(2) = 31, a(n) = 30*a(n-1)-a(n-2)}, a(n), remember):
map(f, [$1..30]); # Robert Israel, Jul 09 2015

CoefficientList[Series[x*(1 + x)/(x^2 - 30 x + 1), {x, 0, 17}], x] (* Michael De Vlieger, Jul 09 2015 *)
LinearRecurrence[{30,-1},{1,31},20] (* Harvey P. Dale, Sep 05 2021 *)

Vec((1+x)/(x^2-30*x+1)+O(x^99)) \\ Charles R Greathouse IV, Sep 25 2012

G.f.: x*(1+x)/(x^2-30*x+1).
a(1) = 1, a(2) = 31, a(n) = 30*a(n-1)-a(n-2) for n>2.
a(n) = ((15-4*sqrt(14))^(n-1)*(7-2*sqrt(14))+(7+2*sqrt(14))*(15+4*sqrt(14))^(n-1))/14. - Gerry Martens, Jul 09 2015

Edited by Alois P. Heinz, Sep 09 2011

A157874 Expansion of 104x^2 / (-x^3+675x^2-675*x+1).

Original entry on oeis.org

0, 104, 70200, 47314800, 31890105104, 21493883525400, 14486845606014600, 9764112444570315104, 6580997300794786365600, 4435582416623241440099400, 2989575967806763935840630104, 2014969766719342269515144590800, 1358086633192868882889271613569200

Offset: 1

Paul Weisenhorn, Mar 08 2009

This sequence is part of a solution of a more general problem involving two equations, three sequences a(n), b(n), c(n) and a constant A:
    A    * c(n)+1 = a(n)^2,
   (A+1) * c(n)+1 = b(n)^2, for details see comment in A157014.
A157874 is the c(n) sequence for A=6.

Colin Barker, Table of n, a(n) for n = 1..350
Index entries for linear recurrences with constant coefficients, signature (675,-675,1).

6*A157874(n)+1 = A153111(n)^2.

7*A157874(n)+1 = A157461(n)^2.

Rest[CoefficientList[Series[104x^2/(-x^3+675x^2-675x+1),{x,0,20}],x]] (* or *) LinearRecurrence[{675,-675,1},{0,104,70200},20] (* Harvey P. Dale, Oct 04 2015 *)

concat(0, Vec(104*x^2/(-x^3+675*x^2-675*x+1) + O(x^20))) \\ Charles R Greathouse IV, Sep 26 2012

a(n) = -round((337+52*sqrt(42))^(-n)*(-1+(337+52*sqrt(42))^n)*(13+2*sqrt(42)+(-13+2*sqrt(42))*(337+52*sqrt(42))^n))/168 \\ Colin Barker, Jul 25 2016

G.f.: 104*x^2 / (-x^3+675*x^2-675*x+1).
c(1) = 0, c(2) = 104, c(3) = 675*c(2), c(n) = 675 * (c(n-1)-c(n-2)) + c(n-3) for n>3.
a(n) = -((337+52*sqrt(42))^(-n)*(-1+(337+52*sqrt(42))^n)*(13+2*sqrt(42)+(-13+2*sqrt(42))*(337+52*sqrt(42))^n))/168. - Colin Barker, Jul 25 2016

Edited by Alois P. Heinz, Sep 09 2011

A133275 Numbers X such that 30*X^2-45 is a square.

Original entry on oeis.org

3, 63, 1383, 30363, 666603, 14634903, 321301263, 7053992883, 154866542163, 3400009934703, 74645352021303, 1638797734533963, 35978904807725883, 789897108035435463, 17341757471971854303, 380728767275345359203

Offset: 1

Richard Choulet, Oct 16 2007

Positive values of x (or y) satisfying x^2 - 22xy + y^2 + 180 = 0. - Colin Barker, Feb 19 2014

Vincenzo Librandi, Table of n, a(n) for n = 1..200
Index entries for linear recurrences with constant coefficients, signature (22,-1).

Cf. A157014.

I:=[3,63]; [n le 2 select I[n] else 22*Self(n-1)-Self(n-2): n in [1..20]]; // Vincenzo Librandi, Feb 21 2014

CoefficientList[Series[3 (1 - x)/(1 - 22 x + x^2), {x, 0, 40}], x] (* Vincenzo Librandi, Feb 21 2014 *)

a(n+2) = 22*a(n+1)-a(n).
a(n+1) = 11*a(n)+2*(30*a(n)^2-45)^0.5.
G.f.: -3*x*(-1+x)/(1-22*x+x^2). - R. J. Mathar, Nov 14 2007
a(n) = 3*A157014(n). - Colin Barker, Feb 19 2014

More terms from Paolo P. Lava, Aug 06 2008

cp's OEIS Frontend

A238379 Expansion of (1 - x)/(1 - 36*x + x^2).

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A157877 Expansion of (1-x)*x/(x^2-30*x+1).

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A157879 Expansion of 120*x^2 / (-x^3+899*x^2-899*x+1).

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A153111 Solutions of the Pell-like equation 1 + 6*A*A = 7*B*B, with A, B integers.

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A133283 Numbers k such that 30*k^2 + 6 is a square.

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A157459 Expansion of 72*x^2 / (1 - 323*x + 323*x^2 - x^3).

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A157877 Expansion of (1-x)x/(x^2-30x+1).

A157879 Expansion of 120x^2 / (-x^3+899x^2-899*x+1).

A153111 Solutions of the Pell-like equation 1 + 6AA = 7BB, with A, B integers.

A157459 Expansion of 72x^2 / (1 - 323x + 323*x^2 - x^3).

A157461 Expansion of x(x+1) / (x^2-26x+1).

A157878 Expansion of x(1+x)/(x^2-30x+1).

A157874 Expansion of 104x^2 / (-x^3+675x^2-675*x+1).