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.

A285349 Expansion of r(q)^2 / r(q^2) in powers of q where r() is the Rogers-Ramanujan continued fraction.

Original entry on oeis.org

1, -2, 4, -4, 2, 2, -8, 12, -12, 6, 8, -24, 36, -36, 16, 20, -62, 92, -88, 40, 46, -144, 208, -196, 88, 102, -308, 440, -412, 180, 208, -624, 884, -816, 356, 404, -1206, 1692, -1552, 672, 760, -2244, 3128, -2852, 1224, 1378, -4048, 5612, -5084, 2174, 2428, -7104, 9796, -8836, 3760
Offset: 0

Views

Author

Seiichi Manyama, Apr 17 2017

Keywords

Comments

Let k(q) = r(q) * r(q^2)^2.
G.f. satisfies: A(q) = (1 - k(q))/(1 + k(q)).
And r(q)^5 = k(q) * A(q)^2.

Links

Crossrefs

r(q)^k / r(q^k): this sequence (k=2), A285628 (k=3), A285629 (k=4), A285630 (k=5).
Cf. A007325, A078905 (r(q)^5), A112274 (k(q)), A285348.

Formula

a(n) = A138518(n) + A285348(n) for n>0 (conjectured). - Thomas Baruchel, May 14 2018

A285583 Expansion of r(q^3) / r(q)^3 in powers of q where r() is the Rogers-Ramanujan continued fraction.

Original entry on oeis.org

1, 3, 3, -3, -9, -3, 15, 18, -12, -42, -12, 63, 72, -45, -153, -51, 195, 228, -123, -435, -144, 540, 621, -321, -1140, -393, 1332, 1536, -747, -2700, -924, 3084, 3528, -1683, -6063, -2097, 6714, 7668, -3549, -12843, -4425, 14004, 15894, -7263, -26208, -9057
Offset: 0

Views

Author

Seiichi Manyama, Apr 22 2017

Keywords

Links

Crossrefs

r(q^k) / r(q)^k: A285348 (k=2), this sequence (k=3), A285584 (k=4), A285585 (k=5).
Cf. A055102, A285443, A285628.

A285629 Expansion of r(q)^4 / r(q^4) in powers of q where r() is the Rogers-Ramanujan continued fraction.

Original entry on oeis.org

1, -4, 10, -16, 16, -4, -20, 48, -66, 60, -18, -64, 168, -248, 236, -80, -208, 536, -750, 688, -252, -528, 1432, -2048, 1908, -724, -1356, 3648, -5104, 4680, -1820, -3088, 8510, -12000, 11044, -4368, -6940, 19112, -26632, 24304, -9734, -14584, 40656, -56784, 51840
Offset: 0

Views

Author

Seiichi Manyama, Apr 22 2017

Keywords

Links

Crossrefs

r(q)^k / r(q^k): A285349 (k=2), A285628 (k=3), this sequence (k=4), A285630 (k=5).
Cf. A285584.

A285630 Expansion of r(q)^5 / r(q^5) in powers of q where r() is the Rogers-Ramanujan continued fraction.

Original entry on oeis.org

1, -5, 15, -30, 40, -25, -35, 140, -250, 285, -150, -210, 740, -1230, 1330, -675, -880, 3015, -4830, 5025, -2450, -3135, 10380, -16180, 16450, -7875, -9785, 31850, -48720, 48600, -22800, -27985, 89465, -134760, 132530, -61400, -74205, 234515, -349000, 339145
Offset: 0

Views

Author

Seiichi Manyama, Apr 22 2017

Keywords

Comments

G.f. A(q) satisfies: A(q) = u^5 / v = (v^4 - 3*v^3 + 4*v^2 - 2*v + 1) / (v^4 + 2*v^3 + 4*v^2 + 3*v + 1), where u = r(q) and v = r(q^5).

Links

Crossrefs

r(q)^k / r(q^k): A285349 (k=2), A285628 (k=3), A285629 (k=4), this sequence (k=5).
Cf. A078905 (u^5), A229793 (1 / u^5), A285585, A285587.
Showing 1-4 of 4 results.

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

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