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.

A285348 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, 0, -4, -2, 6, 8, -4, -16, -6, 20, 24, -12, -44, -16, 52, 62, -28, -108, -40, 122, 144, -64, -244, -88, 266, 308, -136, -508, -180, 544, 624, -272, -1008, -356, 1060, 1206, -524, -1920, -672, 1988, 2244, -968, -3524, -1224, 3606, 4048, -1732, -6284
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^2)^5 = k(q)^2 * A(q).

Links

Crossrefs

r(q^k) / r(q)^k: this sequence (k=2), A285583 (k=3), A285584 (k=4), A285585 (k=5).
Cf. A007325, A078905 (r(q)^5), A112274 (k(q)), A112803 (1 + k(q)), A285349, A285355 (k(q)^2).

Formula

a(n) = A285349(n) - A138518(n) for n>0 (conjectured). - Thomas Baruchel, May 14 2018

A285585 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, 10, 5, -15, -25, 10, 60, 25, -110, -150, 85, 360, 155, -505, -675, 330, 1410, 555, -1925, -2450, 1210, 4920, 1930, -6275, -7875, 3710, 15000, 5720, -18575, -22800, 10735, 42310, 15960, -50605, -61400, 28280, 110610, 41100, -129570, -155250, 71060, 274320
Offset: 0

Views

Author

Seiichi Manyama, Apr 22 2017

Keywords

Comments

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

Links

Crossrefs

r(q^k) / r(q)^k: A285348 (k=2), A285583 (k=3), A285584 (k=4), this sequence (k=5).
Cf. A078905 (u^5), A229793 (1 / u^5), A285587, A285630.

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.
Showing 1-4 of 4 results.

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

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