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 1-10 of 13 results. Next

A067570 Numbers n such that A000009(n) divides A067553(n).

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 7
Offset: 1

Views

Author

Naohiro Nomoto, Jan 30 2002

Keywords

Crossrefs

Cf. A067553, A000009.

A265820 Expansion of Product_{k>=1} 1/(1 - (3*k-1)*x^(3*k-1)).

Original entry on oeis.org

1, 0, 2, 0, 4, 5, 8, 10, 24, 20, 73, 51, 146, 142, 306, 409, 731, 835, 1662, 1828, 3969, 4251, 8256, 9525, 17814, 22565, 38629, 47424, 82916, 101387, 185271, 218421, 386140, 468783, 806005, 1040428, 1696283, 2160026, 3567221, 4498026, 7683250, 9446666
Offset: 0

Views

Author

Vaclav Kotesovec, Dec 15 2015

Keywords

Links

Crossrefs

Cf. A067553, A265821.

Programs

  • Mathematica
    nmax = 40; CoefficientList[Series[Product[1/(1 - (3*k-1)*x^(3*k-1)), {k, 1, nmax}], {x, 0, nmax}], x]

Formula

a(n) ~ c * 2^(n/2), where
c = 14.317325023208603416271945494838289608390197678435231... if n is even,
c = 13.388403642510880418401945468592189683402616378443965... if n is odd.

A265821 Expansion of Product_{k>=1} 1/(1 - (3*k-2)*x^(3*k-2)).

Original entry on oeis.org

1, 1, 1, 1, 5, 5, 5, 12, 28, 28, 38, 66, 130, 143, 232, 344, 616, 738, 1094, 1561, 2840, 3671, 5117, 7227, 12833, 16182, 22428, 32205, 57058, 71006, 98684, 141253, 241563, 301889, 421994, 610113, 1018507, 1278706, 1784671, 2549610, 4224964, 5333003, 7491698
Offset: 0

Views

Author

Vaclav Kotesovec, Dec 15 2015

Keywords

Links

Crossrefs

Cf. A067553, A265820.

Programs

  • Mathematica
    nmax = 40; CoefficientList[Series[Product[1/(1 - (3*k-2)*x^(3*k-2)), {k, 1, nmax}], {x, 0, nmax}], x]

Formula

a(n) ~ c * 2^(n/2), where
c = 4.633065657780064798394952757560310709647495826095820632429... if mod(n,4) = 0
c = 4.169885941972377533366541853673119715620037601993736640548... if mod(n,4) = 1
c = 4.088913297791237602600754017373520586356446410096065167531... if mod(n,4) = 2
c = 4.069986547973463713613958049535085419215417774875202440925... if mod(n,4) = 3.

A265828 Expansion of Product_{k>=1} 1/(1 - (4*k-1)*x^(4*k-1)).

Original entry on oeis.org

1, 0, 0, 3, 0, 0, 9, 7, 0, 27, 21, 11, 81, 63, 82, 258, 189, 246, 851, 586, 738, 2896, 1984, 2237, 8688, 6491, 7009, 26091, 21874, 22609, 78868, 65653, 71600, 240021, 197686, 231642, 731137, 599038, 696146, 2219861, 1821033, 2098301, 6778660, 5540660
Offset: 0

Views

Author

Vaclav Kotesovec, Dec 16 2015

Keywords

Links

Crossrefs

Cf. A067553, A265820, A265821, A265829, A265830.

Programs

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

Formula

a(n) ~ c * 3^(n/3), where
c = 1.440862416741436228307395343405986172843082997125243989739... if mod(n,3) = 0
c = 0.839303125100473007517704405672941818726137049977537857220... if mod(n,3) = 1
c = 0.669924376359406710094617326814984989681716404092521759237... if mod(n,3) = 2.

A265829 Expansion of Product_{k>=1} 1/(1 - (4*k-2)*x^(4*k-2)).

Original entry on oeis.org

1, 0, 2, 0, 4, 0, 14, 0, 28, 0, 66, 0, 168, 0, 350, 0, 760, 0, 1754, 0, 3692, 0, 7766, 0, 17076, 0, 35282, 0, 73232, 0, 156758, 0, 320768, 0, 658978, 0, 1380612, 0, 2808534, 0, 5732780, 0, 11849002, 0, 23997576, 0, 48701918, 0, 99744056, 0, 201405042
Offset: 0

Views

Author

Vaclav Kotesovec, Dec 16 2015

Keywords

Links

Crossrefs

Cf. A067553, A265820, A265821, A265828, A265830.

Programs

  • Mathematica
    nmax = 40; CoefficientList[Series[Product[1/(1 - (4*k-2)*x^(4*k-2)), {k, 1, nmax}], {x, 0, nmax}], x]

Formula

If n is even, then a(n) ~ c * 2^(n/2), where c = 6.8748052998532604456256851165148110527112306899116599334584... .

A265830 Expansion of Product_{k>=1} 1/(1 - (4*k-3)*x^(4*k-3)).

Original entry on oeis.org

1, 1, 1, 1, 1, 6, 6, 6, 6, 15, 40, 40, 40, 53, 98, 223, 223, 240, 386, 611, 1236, 1257, 1459, 2189, 3314, 6464, 6891, 8630, 12280, 17934, 34094, 37282, 45977, 64260, 93317, 177015, 199516, 243028, 335386, 486558, 914525, 1027071, 1246171, 1717917, 2499859
Offset: 0

Views

Author

Vaclav Kotesovec, Dec 16 2015

Keywords

Links

Crossrefs

Cf. A067553, A265820, A265821, A265828, A265829.

Programs

  • Mathematica
    nmax = 40; CoefficientList[Series[Product[1/(1 - (4*k-3)*x^(4*k-3)), {k, 1, nmax}], {x, 0, nmax}], x]

Formula

a(n) ~ c * 5^(n/5), where
c = 2.507825733169876852324734244164361344346137946210165985160... if mod(n,5) = 0
c = 2.044059357237393849525094744007074653835911858380855756712... if mod(n,5) = 1
c = 1.804839638762776493150118361894215102701328815651225876275... if mod(n,5) = 2
c = 1.804038421648852594778176511112001297019074444232793470829... if mod(n,5) = 3
c = 1.892664578176041496503561133229019191251461591133509951564... if mod(n,5) = 4.

A265831 Expansion of Product_{k>=1} 1/(1 - (5*k-1)*x^(5*k-1)).

Original entry on oeis.org

1, 0, 0, 0, 4, 0, 0, 0, 16, 9, 0, 0, 64, 36, 14, 0, 256, 144, 137, 19, 1024, 576, 548, 202, 4120, 2304, 2192, 1537, 16847, 9245, 8768, 6148, 68522, 37462, 35106, 24592, 280649, 153151, 141382, 98407, 1122596, 622810, 572610, 394796, 4490428, 2550289, 2320167
Offset: 0

Views

Author

Vaclav Kotesovec, Dec 16 2015

Keywords

Links

Crossrefs

Cf. A067553, A265820, A265821, A265828, A265829, A265830.
Cf. A265832, A265833, A265834.

Programs

  • Mathematica
    nmax = 40; CoefficientList[Series[Product[1/(1 - (5*k-1)*x^(5*k-1)), {k, 1, nmax}], {x, 0, nmax}], x]

Formula

a(n) ~ c * 4^(n/4), where
c = 1.073840819469157289995715447280332198042213811468819293923... if mod(n,4) = 0
c = 0.431347264451907652131063891031332936177772975542057097666... if mod(n,4) = 1
c = 0.283892524489889292147114138438462508437169743150135175791... if mod(n,4) = 2
c = 0.139829615705558896416806329024657454417365487147024035166... if mod(n,4) = 3.

A265832 Expansion of Product_{k>=1} 1/(1 - (5*k-2)*x^(5*k-2)).

Original entry on oeis.org

1, 0, 0, 3, 0, 0, 9, 0, 8, 27, 0, 24, 81, 13, 72, 243, 103, 216, 747, 309, 648, 2345, 927, 1967, 7547, 2781, 6214, 22641, 8371, 19474, 67923, 25531, 62518, 203802, 79097, 187554, 612253, 243947, 562700, 1842300, 764609, 1689142, 5546932, 2293870, 5077244
Offset: 0

Views

Author

Vaclav Kotesovec, Dec 16 2015

Keywords

Links

Crossrefs

Cf. A067553, A265820, A265821, A265828, A265829, A265830.
Cf. A265831, A265833, A265834.

Programs

  • Mathematica
    nmax = 40; CoefficientList[Series[Product[1/(1 - (5*k-2)*x^(5*k-2)), {k, 1, nmax}], {x, 0, nmax}], x]

Formula

a(n) ~ c * 3^(n/3), where
c = 1.171555591294550584937080627149625982761747171861533383233... if mod(n,3) = 0
c = 0.337047816440008855542662141834272219461954848118918717600... if mod(n,3) = 1
c = 0.518706292284531581251050944157928147536875425948432140453... if mod(n,3) = 2.

A265833 Expansion of Product_{k>=1} 1/(1 - (5*k-3)*x^(5*k-3)).

Original entry on oeis.org

1, 0, 2, 0, 4, 0, 8, 7, 16, 14, 32, 28, 76, 56, 201, 112, 402, 241, 804, 566, 1608, 1475, 3238, 2950, 6739, 5900, 14066, 11827, 30533, 24012, 61066, 49865, 122164, 103846, 245070, 224499, 494374, 449035, 1001635, 898992, 2032082, 1805626, 4181855, 3640890
Offset: 0

Views

Author

Vaclav Kotesovec, Dec 16 2015

Keywords

Links

Crossrefs

Cf. A067553, A265820, A265821, A265828, A265829, A265830.
Cf. A265831, A265832, A265834.

Programs

  • Mathematica
    nmax = 40; CoefficientList[Series[Product[1/(1 - (5*k-3)*x^(5*k-3)), {k, 1, nmax}], {x, 0, nmax}], x]

Formula

a(n) ~ c * 2^(n/2), where
c = 2.083307142076305100818196347525098347528893162823662452462... if n is even,
c = 1.350596787589129261746699661559125050005090208149022621867... if n is odd.

A265834 Expansion of Product_{k>=1} 1/(1 - (5*k-4)*x^(5*k-4)).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 7, 7, 7, 7, 7, 18, 54, 54, 54, 54, 70, 136, 352, 352, 352, 373, 590, 986, 2282, 2282, 2308, 2610, 3912, 6288, 14064, 14095, 14738, 17881, 25693, 39949, 86641, 87449, 93243, 112101, 158973, 244550, 525900, 536105, 585510, 698658, 979936
Offset: 0

Views

Author

Vaclav Kotesovec, Dec 16 2015

Keywords

Links

Crossrefs

Cf. A067553, A265820, A265821, A265828, A265829, A265830.
Cf. A265831, A265832, A265833.

Programs

  • Mathematica
    nmax = 40; CoefficientList[Series[Product[1/(1 - (5*k-4)*x^(5*k-4)), {k, 1, nmax}], {x, 0, nmax}], x]

Formula

a(n) ~ c * 6^(n/6), where
c = 1.946161573585465742120451753889110403102785483969509157884... if mod(n,6) = 0
c = 1.492695368258335848636116399838163314228018468452433528714... if mod(n,6) = 1
c = 1.205892633747241909081118546347785156858709648302505136919... if mod(n,6) = 2
c = 1.062580541177612790307764142722360963628515836057478463493... if mod(n,6) = 3
c = 1.098873691517923934789388233817534832428257891275964607033... if mod(n,6) = 4
c = 1.239744254161848837318727201496086964789190390884460407810... if mod(n,6) = 5.
Showing 1-10 of 13 results. Next

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

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