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.

Previous Showing 11-15 of 15 results.

A327757 Expansion of Product_{k>=1} (1 - x^k)^(3/k), where (m/n) is the Kronecker symbol.

Original entry on oeis.org

1, -1, 1, -1, 0, 1, -1, 2, -1, 0, 0, -2, 2, -2, 2, 0, -2, 3, -5, 4, -2, 0, 4, -6, 7, -6, 4, 1, -4, 8, -10, 8, -4, -2, 9, -13, 14, -12, 3, 4, -14, 20, -21, 17, -8, -6, 19, -28, 31, -23, 10, 10, -28, 41, -41, 32, -10, -16, 40, -58, 58, -44, 13, 24, -61, 81, -84, 59, -16, -37, 84
Offset: 0

Views

Author

Seiichi Manyama, Sep 24 2019

Keywords

Links

Crossrefs

Product_{k>=1} (1 - x^k)^(b/k): A092869 (b=2), A081362 (b=4), A007325 (b=5), A092876 (b=13).
Cf. A091338, A327758.

Programs

  • PARI
    N=66; x='x+O('x^N); Vec(prod(k=1, N, (1-x^k)^kronecker(3, k)))

A296202 Expansion of 1/(1 + x/(1 + x/(1 + x^2/(1 + x/(1 + x^3/(1 + x/(1 + x^4/(1 + ...)))))))), a continued fraction.

Original entry on oeis.org

1, -1, 2, -4, 7, -11, 16, -22, 28, -30, 18, 29, -152, 427, -988, 2060, -4002, 7354, -12868, 21472, -34054, 50838, -69920, 84186, -75275, 2395, 217417, -742554, 1860191, -4067099, 8183154, -15493168, 27886577, -47905049, 78485095, -121944988, 177329498, -234464309, 261801461, -183121605, -164852147
Offset: 0

Views

Author

Ilya Gutkovskiy, Dec 07 2017

Keywords

Crossrefs

Cf. A007325, A092869, A129509, A292799, A292854, A296201.

Programs

  • Mathematica
    nmax = 40; CoefficientList[Series[1/(1 + ContinuedFractionK[x^(1 + k (1 + (-1)^k)/4), 1, {k, 0, nmax}]), {x, 0, nmax}], x]

A301410 G.f. A(x) satisfies: A(x) = 1/(1 + x*A(x) + x^2*A(x)/(1 + x^3*A(x) + x^4*A(x)/(1 + x^5*A(x) + x^6*A(x)/(1 + ...)))), a continued fraction.

Original entry on oeis.org

1, -1, 1, -1, 1, 0, -3, 10, -26, 60, -127, 250, -458, 766, -1107, 1146, 188, -5782, 22658, -66620, 170841, -400001, 869124, -1755912, 3263352, -5403598, 7264938, -4950248, -13623003, 80819359, -275474805, 775529946, -1954651995, 4537336510, -9788453019, 19563409996
Offset: 0

Views

Author

Ilya Gutkovskiy, Mar 20 2018

Keywords

Examples

			G.f. A(x) = 1 - x + x^2 - x^3 + x^4 - 3*x^6 + 10*x^7 - 26*x^8 + 60*x^9 - 127*x^10 + ...

Crossrefs

Cf. A092869, A301362.

A292869 Expansion of 1/(1 + x + x^2 + x^3/(1 + x^4 + x^5 + x^6/(1 + x^7 + x^8 + x^9/(1 + ...)))), a continued fraction.

Original entry on oeis.org

1, -1, 0, 0, 1, -1, 0, 1, 0, -1, -1, 2, -1, -1, 1, 3, -2, -2, 2, 1, -5, -1, 7, 1, -5, 2, 7, -9, -10, 6, 10, -10, 2, 22, 2, -29, -6, 18, -19, -22, 39, 52, -30, -27, 32, -19, -108, -2, 125, 29, -43, 101, 90, -215, -231, 83, 89, -126, 186, 522, 28, -523, -167, 18, -598, -336, 1042, 1134, -165, -132, 401
Offset: 0

Views

Author

Ilya Gutkovskiy, Sep 25 2017

Keywords

Crossrefs

Cf. A088353, A092869.

Programs

  • Mathematica
    nmax = 70; CoefficientList[Series[1/(1 + x + x^2 + ContinuedFractionK[x^(3 k - 3), 1 + x^(3 k - 2) + x^(3 k - 1), {k, 2, nmax}]), {x, 0, nmax}], x]

A301411 G.f. A(x) satisfies: A(x) = 1/(1 - x*A(x) - x*A(x)^2/(1 - x*A(x)^3 - x*A(x)^4/(1 - x*A(x)^5 - x*A(x)^6/(1 - ...)))), a continued fraction.

Original entry on oeis.org

1, 2, 12, 108, 1192, 14848, 200432, 2866752, 42853392, 663565616, 10579117744, 172911177584, 2888445810864, 49203276384624, 853289008064304, 15047071017842928, 269585532569464752, 4904425594952671344, 90570287337341726256, 1697589267552262891760, 32295562088556275945136
Offset: 0

Views

Author

Ilya Gutkovskiy, Mar 20 2018

Keywords

Examples

			G.f. A(x) = 1 + 2*x + 12*x^2 + 108*x^3 + 1192*x^4 + 14848*x^5 + 200432*x^6 + 2866752*x^7 + 42853392*x^8 + ...

Crossrefs

Cf. A088352, A092869, A192737, A301410.
Previous Showing 11-15 of 15 results.

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

Content is available under The OEIS End-User License Agreement.