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

A285584 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, 6, 0, -12, -12, 12, 32, 2, -60, -54, 64, 152, 24, -228, -224, 180, 488, 94, -688, -680, 528, 1448, 336, -1884, -1932, 1276, 3744, 944, -4680, -4828, 3088, 9154, 2464, -10980, -11520, 6744, 20792, 5832, -24304, -25618, 14584, 45424, 13184, -51696, -54972
Offset: 0

Views

Author

Seiichi Manyama, Apr 22 2017

Keywords

Links

Crossrefs

r(q^k) / r(q)^k: A285348 (k=2), A285583 (k=3), this sequence (k=4), A285585 (k=5).
Cf. A055103, A285444, A285629.

A285628 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, 6, -6, 0, 12, -24, 27, -15, -12, 48, -81, 90, -54, -36, 159, -258, 267, -138, -123, 441, -684, 693, -354, -318, 1122, -1701, 1668, -801, -792, 2616, -3876, 3753, -1782, -1776, 5778, -8451, 8046, -3705, -3843, 12120, -17496, 16506, -7524, -7848, 24483
Offset: 0

Views

Author

Seiichi Manyama, Apr 22 2017

Keywords

Links

Crossrefs

r(q)^k / r(q^k): A285349 (k=2), this sequence (k=3), A285629 (k=4), A285630 (k=5).
Cf. A285583.

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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