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.

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

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.

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.

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.

A285587 Expansion of v * (v^4 - 3*v^3 + 4*v^2 - 2*v + 1) in powers of q where r() is the Rogers-Ramanujan continued fraction and v = r(q^5).

Original entry on oeis.org

0, 1, -2, 4, -3, 1, -1, 4, -12, 12, -5, 1, -6, 24, -30, 15, 0, 4, -28, 48, -30, -1, 2, 12, -45, 40, 1, -8, 24, 0, -26, -1, 12, -68, 90, -30, 1, -12, 96, -192, 125, 0, 6, -84, 243, -220, -1, 4, 24, -180, 245, 2, -18, 84, -36, -124, -3, 32, -216, 384, -180, 2, -34, 308
Offset: 0

Views

Author

Seiichi Manyama, Apr 22 2017

Keywords

Comments

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

Crossrefs

Cf. A078905 (r(q)^5), A285585.
Showing 1-5 of 5 results.

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