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 1-5 of 5 results.

A285381 G.f.: 1/(1 - 1!*x/(1 - 2!*x^2/(1 - 3!*x^3/(1 - 4!*x^4/(1 - 5!*x^5/(1 - 6!*x^6/(1 - ...))))))), a continued fraction.

Original entry on oeis.org

1, 1, 1, 3, 5, 11, 33, 67, 169, 435, 1265, 3035, 8025, 22243, 60721, 191307, 491657, 1404371, 4089633, 12183835, 36872377, 126189219, 350136977, 1062359147, 3386475177, 10757830387, 36121721857, 120817807419, 482847966617, 1391650703939, 4654331013489
Offset: 0

Views

Author

Ilya Gutkovskiy, Apr 17 2017

Keywords

Examples

			G.f.: A(x) = 1 + x + x^2 + 3*x^3 + 5*x^4 + 11*x^5 + 33*x^6 + 67*x^7 + 169*x^8 + ...

Links

Crossrefs

Cf. A000142, A088357, A285380.

Programs

  • Mathematica
    nmax = 30; CoefficientList[Series[1/(1 + ContinuedFractionK[-k! x^k, 1, {k, 1, nmax}]), {x, 0, nmax}], x]
  • PARI
    a(n) = my(A=1+O(x)); for(i=1, n, A=1-(n-i+1)!*x^(n-i+1)/A); polcoef(1/A, n); \\ Seiichi Manyama, Apr 16 2021

A292855 Expansion of 1/(1 - x - 2*x^2/(1 - 3*x^3 - 4*x^4/(1 - 5*x^5 - 6*x^6/(1 - 7*x^7 - 8*x^8/(1 - ...))))), a continued fraction.

Original entry on oeis.org

1, 1, 3, 5, 11, 27, 63, 143, 341, 799, 1865, 4417, 10401, 24433, 57619, 135749, 319683, 753427, 1775207, 4182359, 9855389, 23222687, 54718921, 128937361, 303821873, 715906625, 1686933723, 3975020013, 9366551195, 22070960907, 52007117407, 122547413479, 288765804957, 680436157615
Offset: 0

Views

Author

Ilya Gutkovskiy, Sep 25 2017

Keywords

Crossrefs

Cf. A088352, A088357.

Programs

  • Mathematica
    nmax = 33; CoefficientList[Series[1/(1 - x + ContinuedFractionK[-2 k x^(2 k), 1 - (2 k + 1) x^(2 k + 1), {k, 1, nmax}]), {x, 0, nmax}], x]

Formula

a(n) ~ c * d^n, where d = 2.35636016857596143712421472862749989350673596686819... and c = 0.353844135039289092297842723019941866883167102736... - Vaclav Kotesovec, Sep 25 2017

A285409 G.f.: 1/(1 + x/(1 + 2*x^2/(1 + 3*x^3/(1 + 4*x^4/(1 + 5*x^5/(1 + 6*x^6/(1 + ... ))))))), a continued fraction.

Original entry on oeis.org

1, -1, 1, 1, -3, 1, -1, 5, 3, -13, 19, -41, 9, 55, -55, 113, -99, 65, -113, -491, 843, -245, -325, 1295, -783, -121, -887, -287, 2685, -6911, 7559, 12413, -36669, 12179, 42211, -59681, 55281, -22313, 38633, 19361, -465579, 877913, -711185, -575339, 2540955, -3065165, 1681907, -29953, -1287375, 7293527, -19374047
Offset: 0

Views

Author

Ilya Gutkovskiy, Apr 18 2017

Keywords

Examples

			G.f.: A(x) = 1 - x + x^2 + x^3 - 3*x^4 + x^5 - x^6 + 5*x^7 + 3*x^8 - 13*x^9 + ...

Crossrefs

Cf. A007325, A088357.

Programs

  • Mathematica
    nmax = 50; CoefficientList[Series[1/(1 + ContinuedFractionK[k x^k, 1, {k, 1, nmax}]), {x, 0, nmax}], x]

A294410 Expansion of 1/(1 - x/(1 - x/(1 - 2*x^2/(1 - 2*x^2/(1 - 3*x^3/(1 - 3*x^3/(1 - ...))))))), a continued fraction.

Original entry on oeis.org

1, 1, 2, 4, 10, 24, 64, 164, 440, 1164, 3128, 8368, 22552, 60624, 163528, 440768, 1189616, 3210000, 8667296, 23400304, 63196192, 170668608, 460972768, 1245085184, 3363190688, 9084616128, 24540062528, 66289885504, 179071151872, 483733046208, 1306740302848, 3529993576448, 9535868752256
Offset: 0

Views

Author

Ilya Gutkovskiy, Oct 30 2017

Keywords

Crossrefs

Cf. A000142, A006958, A088357.

Programs

  • Mathematica
    nmax = 32; CoefficientList[Series[1/(1 + ContinuedFractionK[-Floor[(k + 1)/2] x^Floor[(k + 1)/2], 1, {k, 1, nmax}]), {x, 0, nmax}], x]

Formula

a(n) ~ c * d^n, where d = 2.7014053577058965980816004348205865476643047417470551135866... and c = 0.1473934094237780704912896884660893313026695094814554837... - Vaclav Kotesovec, Sep 16 2021

A343468 G.f.: 1 + 1*x/(1 + 2*x^2/(1 + 3*x^3/(1 + 4*x^4/(1 + 5*x^5/(1 + ...))))).

Original entry on oeis.org

1, 1, 0, -2, 0, 4, 6, -8, -24, -2, 48, 76, -42, -224, -144, 406, 744, -332, -2154, -1400, 4320, 7702, -2016, -21428, -17802, 34216, 76152, -5210, -195816, -181916, 300510, 772432, 53136, -1851770, -2055360, 2388772, 7515246, 1755880, -16586616, -21354266, 19195248, 72641884, 27527118
Offset: 0

Views

Author

Seiichi Manyama, Apr 16 2021

Keywords

Crossrefs

Cf. A000698, A003823, A088357, A343472, A343473.

Programs

  • PARI
    a(n) = my(A=1+O(x)); for(i=1, n, A=1+(n-i+1)*x^(n-i+1)/A); polcoef(A, n);
Showing 1-5 of 5 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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