cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A166912 a(n) = 20*a(n-1) - 64*a(n-2) - 225 for n > 2; a(0) = 106, a(1) = 8075, a(2) = 114235.

Original entry on oeis.org

106, 8075, 114235, 1767675, 28042235, 447713275, 7159562235, 114537594875, 1832539914235, 29320392212475, 469125289738235, 7506000693166075, 120095995320074235, 1921535862038855675, 30744573540292362235
Offset: 0

Views

Author

Klaus Brockhaus, Oct 27 2009

Keywords

Comments

Related to Reverse and Add trajectory of 318 in base 4: A075153(6*n) = 3*a(n).
lim_{n -> infinity} a(n)/a(n-1) = 16.

Links

Crossrefs

Cf. A075153, A166913, A166914, A166915, A166916, A166917, A167120, A167121, A167122.

Programs

  • Mathematica
    Join[{106},LinearRecurrence[{21,-84,64},{8075,114235,1767675},20]] (* Harvey P. Dale, Jun 07 2012 *)
  • PARI
    m=15; v=concat([106, 8075, 114235], vector(m-3)); for(n=4, m, v[n]=20*v[n-1]-64*v[n-2]-225); v

Formula

a(n) = (1280*16^n + 940*4^n - 15)/3 for n > 0.
G.f.: (106 + 5849*x - 46436*x^2 + 40256*x^3)/((1-x)*(1-4*x)*(1-16*x)).
From G. C. Greubel, May 28 2016: (Start)
a(n) = 21*a(n-1) - 84*a(n-2) + 64*a(n-3).
E.g.f.: (1/3)*(-15*exp(x) + 940*exp(4*x) + 1280*exp(16*x)) - 629. (End)

A166913 a(n) = 20*a(n-1) - 64*a(n-2) - 150 for n > 2; a(0) = 357, a(1) = 14450, a(2) = 221650.

Original entry on oeis.org

357, 14450, 221650, 3508050, 55975250, 894989650, 14317376850, 229068199250, 3665051866450, 58640672576850, 938250132084050, 15011999596762450, 240191983481869650, 3843071695444596050, 61489146966052263250
Offset: 0

Views

Author

Klaus Brockhaus, Oct 27 2009

Keywords

Comments

Related to Reverse and Add trajectory of 318 in base 4: A075153(6*n+1) = 3*a(n).
lim_{n -> infinity} a(n)/a(n-1) = 16.

Links

Crossrefs

Cf. A075153, A166912, A166914, A166915, A166916, A166917, A167120, A167121, A167122.

Programs

  • Mathematica
    Join[{357},LinearRecurrence[{21,-84,64},{14450,221650,3508050},20]] (* Harvey P. Dale, Jun 18 2014 *)
  • PARI
    m=15; v=concat([357, 14450, 221650], vector(m-3)); for(n=4, m, v[n]=20*v[n-1]-64*v[n-2]-150); v

Formula

a(n) = (2560*16^n + 600*4^n - 10)/3 for n > 0.
G.f.: (357 + 6953*x - 51812*x^2 + 44352*x^3)/((1-x)*(1-4*x)*(1-16*x)).
a(0)=357, a(1)=14450, a(2)=221650, a(3)=3508050, a(n)=21*a(n-1)- 84*a(n-2)+ 64*a(n-3). - Harvey P. Dale, Jun 18 2014
E.g.f.: (1/3)*(-10*exp(x) + 600*exp(4*x) + 2560*exp(16*x)) - 693. - G. C. Greubel, May 28 2016

A167121 a(n) = 20*a(n-1) - 64*a(n-2) + 2 for n > 2; a(0) = 1, a(1) = 22, a(2) = 377.

Original entry on oeis.org

1, 22, 377, 6134, 98554, 1578506, 25262666, 404228938, 6467768138, 103484710730, 1655757053770, 26492119588682, 423873940332362, 6781983152971594, 108511730878160714, 1736187695773032266, 27779003139258359626
Offset: 0

Views

Author

Klaus Brockhaus, Oct 27 2009

Keywords

Comments

lim_{n -> infinity} a(n)/a(n-1) = 16.

Links

Crossrefs

Cf. A166912, A166913, A167120, A167122.

Programs

  • Magma
    [ n le 2 select 21*n-20 else n eq 3 select 377 else 20*Self(n-1)-64*Self(n-2)+2: n in [1..17] ];
  • Mathematica
    CoefficientList[Series[(1 + x - x^2 + x^3)/((1-x)*(1-4*x)*(1-16*x)), {x, 0, 10}], x] (* G. C. Greubel, Jun 04 2016 *)
Join[{1},RecurrenceTable[{a[1]==22,a[2]==377,a[n]==20a[n-1]-64a[n-2]+2}, a,{n,20}]] (* Harvey P. Dale, Apr 01 2019 *)

Formula

a(n) = (4337*16^n - 1540*4^n + 128)/2880, for n > 0.
G.f.: (1 + x - x^2 + x^3)/((1-x)*(1-4*x)*(1-16*x)).
E.g.f.: (1/2880)*(-45 + 128*exp(x) - 1540*exp(4*x) + 4337*exp(16*x)). - G. C. Greubel, Jun 04 2016

A167122 a(n) = 20*a(n-1) - 64*a(n-2) + 3 for n > 2; a(0) = 1, a(1) = 22, a(2) = 378.

Original entry on oeis.org

1, 22, 378, 6155, 98911, 1584303, 25355759, 405719791, 6491627247, 103866478319, 1661865422575, 26589853839087, 425437689736943, 6807003149037295, 108912050837581551, 1742592815213244143, 27881485050659663599
Offset: 0

Views

Author

Klaus Brockhaus, Oct 27 2009

Keywords

Comments

lim_{n -> infinity} a(n)/a(n-1) = 16.

Links

Crossrefs

Cf. A166912, A166913, A167120, A167121.

Programs

  • Magma
    [ n le 2 select 21*n-20 else n eq 3 select 378 else 20*Self(n-1)-64*Self(n-2)+3: n in [1..17] ];
  • Mathematica
    CoefficientList[Series[(1 + x + x^3)/((1-x)*(1-4*x)*(1-16*x)), {x, 0, 10}], x] (* G. C. Greubel, Jun 04 2016 *)
LinearRecurrence[{21,-84,64},{1,22,378,6155},20] (* Harvey P. Dale, Sep 26 2023 *)

Formula

a(n) = (1451*16^n - 540*4^n + 64)/960, for n > 0.
G.f.: (1 + x + x^3)/((1-x)*(1-4*x)*(1-16*x)).
E.g.f.: (1/960)*(-15 + 64*exp(x) - 540*exp(4*x) + 1451*exp(16*x)). - G. C. Greubel, Jun 04 2016
Showing 1-4 of 4 results.

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