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.

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A100179 Structured heptagonal diamond numbers (vertex structure 5).

Original entry on oeis.org

1, 9, 34, 86, 175, 311, 504, 764, 1101, 1525, 2046, 2674, 3419, 4291, 5300, 6456, 7769, 9249, 10906, 12750, 14791, 17039, 19504, 22196, 25125, 28301, 31734, 35434, 39411, 43675, 48236, 53104
Offset: 1

Views

Author

James A. Record (james.record(AT)gmail.com), Nov 07 2004

Keywords

Links

Crossrefs

Cf. A004126 = alternate vertex; A000447 = structured diamonds; A100145 for more on structured numbers.

Programs

  • Magma
    [(1/6)*(10*n^3-9*n^2+5*n): n in [1..40]]; // Vincenzo Librandi, Aug 18 2011
  • Mathematica
    Table[(10n^3-9n^2+5n)/6,{n,40}] (* Harvey P. Dale, Oct 28 2018 *)
  • PARI
    vector(40, n, (10*n^3-9*n^2+5*n)/6) \\ G. C. Greubel, Nov 08 2018

Formula

a(n) = (1/6)*(10*n^3 - 9*n^2 + 5*n).
G.f.: x*(1 + 5*x + 4*x^2)/(1-x)^4. - Colin Barker, Jan 19 2012
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - Harvey P. Dale, Oct 28 2018
E.g.f.: (6*x + 21*x^2 + 10*x^3)*exp(x)/6. - G. C. Greubel, Nov 08 2018

A100186 Structured heptagonal anti-diamond numbers (vertex structure 7).

Original entry on oeis.org

1, 16, 67, 176, 365, 656, 1071, 1632, 2361, 3280, 4411, 5776, 7397, 9296, 11495, 14016, 16881, 20112, 23731, 27760, 32221, 37136, 42527, 48416, 54825, 61776, 69291, 77392, 86101, 95440, 105431, 116096
Offset: 1

Views

Author

James A. Record (james.record(AT)gmail.com), Nov 07 2004

Keywords

Links

Crossrefs

Cf. A063521 = alternate vertex; A100188 = structured anti-diamonds; A100145 for more on structured numbers.

Programs

  • Magma
    [(1/6)*(22*n^3-24*n^2+8*n): n in [1..40]]; // Vincenzo Librandi, Aug 18 2011
  • Mathematica
    Table[(22*n^3 - 24*n^2 + 8*n)/6, {n,1,40}] (* or *) LinearRecurrence[{4, -6, 4, -1}, {1, 16, 67, 176}, 40] (* G. C. Greubel, Nov 08 2018 *)
  • PARI
    vector(40, n, (22*n^3 -24*n^2 +8*n)/6) \\ G. C. Greubel, Nov 08 2018

Formula

a(n) = (1/6)*(22*n^3 - 24*n^2 + 8*n).
G.f.: x*(1 + 12*x + 9*x^2)/(1-x)^4. - Colin Barker, Jan 19 2012
E.g.f.: (3*x +21*x^2 +11*x^3)*exp(x)/3. - G. C. Greubel, Nov 08 2018

A100187 Structured octagonal anti-diamond numbers (vertex structure 7).

Original entry on oeis.org

1, 18, 77, 204, 425, 766, 1253, 1912, 2769, 3850, 5181, 6788, 8697, 10934, 13525, 16496, 19873, 23682, 27949, 32700, 37961, 43758, 50117, 57064, 64625, 72826, 81693, 91252, 101529, 112550, 124341, 136928
Offset: 1

Views

Author

James A. Record (james.record(AT)gmail.com), Nov 07 2004

Keywords

Links

Crossrefs

Cf. A063523 = alternate vertex; A100188 = structured anti-diamonds; A100145 for more on structured numbers.

Programs

  • Magma
    [(1/6)*(26*n^3-30*n^2+10*n): n in [1..40]]; // Vincenzo Librandi, Aug 18 2011
  • Mathematica
    Table[(26n^3-30n^2+10n)/6,{n,40}] (* or *) LinearRecurrence[{4,-6,4,-1},{1,18,77,204},40] (* Harvey P. Dale, Dec 24 2012 *)
  • PARI
    vector(40, n, (13*n^3 -15*n^2 +5*n)/3) \\ G. C. Greubel, Nov 08 2018

Formula

a(n) = (1/6)*(26*n^3 - 30*n^2 + 10*n).
G.f.: x*(1 + 14*x + 11*x^2)/(1-x)^4. - Colin Barker, Jan 19 2012
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4); a(1)=1, a(2)=18, a(3)=77, a(4)=204. - Harvey P. Dale, Dec 24 2012
E.g.f.: (3*x + 24*x^2 + 13*x^3)*exp(x)/3. - G. C. Greubel, Nov 08 2018

A100189 Equatorial structured meta-anti-diamond numbers, the n-th number from an equatorial structured n-gonal anti-diamond number sequence.

Original entry on oeis.org

1, 6, 27, 92, 245, 546, 1071, 1912, 3177, 4990, 7491, 10836, 15197, 20762, 27735, 36336, 46801, 59382, 74347, 91980, 112581, 136466, 163967, 195432, 231225, 271726, 317331, 368452, 425517, 488970, 559271, 636896
Offset: 1

Views

Author

James A. Record (james.record(AT)gmail.com), Nov 07 2004

Keywords

Examples

			There are no 1- or 2-gonal anti-diamonds, so 1 and (2n+2) are used as the first and second terms since all the sequences begin as such.

Links

Crossrefs

Cf. A000578, A096000, A051673, A005915, A100186, A100187 - "equatorial" structured anti-diamonds; A100188 - "polar" structured meta-anti-diamond numbers; A006484 for other structured meta numbers; and A100145 for more on structured numbers.

Programs

  • Magma
    [(1/6)*(4*n^4-12*n^3+20*n^2-6*n): n in [1..40]]; // Vincenzo Librandi, Aug 18 2011
  • Mathematica
    Table[(4n^4-12n^3+20n^2-6n)/6,{n,40}] (* or *) LinearRecurrence[ {5,-10,10,-5,1},{1,6,27,92,245},40] (* Harvey P. Dale, Jul 05 2011 *)

Formula

a(n) = (1/6)*(4*n^4-12*n^3+20*n^2-6*n).
a(1)=1, a(2)=6, a(3)=27, a(4)=92, a(5)=245, a(n)=5*a(n-1)-10*a(n-2)+ 10*a(n-3)-5*a(n-4)+a(n-5). - Harvey P. Dale, Jul 05 2011
G.f.: x*(1+x)*(1+7*x^2)/(1-x)^5. - Colin Barker, Jan 19 2012

A100167 Structured pentagonal icositetrahedral numbers (vertex structure 13).

Original entry on oeis.org

1, 38, 171, 460, 965, 1746, 2863, 4376, 6345, 8830, 11891, 15588, 19981, 25130, 31095, 37936, 45713, 54486, 64315, 75260, 87381, 100738, 115391, 131400, 148825, 167726, 188163, 210196, 233885, 259290, 286471, 315488
Offset: 1

Views

Author

James A. Record (james.record(AT)gmail.com), Nov 07 2004

Keywords

Links

Crossrefs

Cf. A100168 = alternate vertex; A100145 for more on structured numbers.

Programs

  • Magma
    [(1/6)*(60*n^3-72*n^2+18*n): n in [1..40]]; // Vincenzo Librandi, Jul 26 2011
  • Mathematica
    Table[(60n^3-72n^2+18n)/6,{n,40}] (* or *) LinearRecurrence[{4,-6,4,-1},{1,38,171,460},40] (* Harvey P. Dale, Aug 21 2016 *)

Formula

a(n) = (1/6)*(60*n^3 - 72*n^2 + 18*n).
G.f.: x*(1 + 34*x + 25*x^2)/(1-x)^4. - Colin Barker, Feb 14 2012

A100168 Structured pentagonal icositetrahedral numbers (vertex structure 10).

Original entry on oeis.org

1, 38, 174, 472, 995, 1806, 2968, 4544, 6597, 9190, 12386, 16248, 20839, 26222, 32460, 39616, 47753, 56934, 67222, 78680, 91371, 105358, 120704, 137472, 155725, 175526, 196938, 220024, 244847, 271470, 299956, 330368
Offset: 1

Views

Author

James A. Record (james.record(AT)gmail.com), Nov 07 2004

Keywords

Links

Crossrefs

Cf. A100167 = alternate vertex; A100145 for more on structured numbers.

Programs

  • Magma
    [(1/6)*(63*n^3-81*n^2+24*n): n in [1..40]]; // Vincenzo Librandi, Jul 26 2011
  • Mathematica
    Table[(63n^3-81n^2+24n)/6,{n,40}]
LinearRecurrence[{4,-6,4,-1},{1,38,174,472},40] (* or *) CoefficientList[ Series[(1+34x+28x^2)/(-1+x)^4,{x,0,40}],x](* Harvey P. Dale, Dec 18 2011 *)

Formula

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4); a(1)=1, a(2)=38, a(3)=174, a(4)=472. - Harvey P. Dale, Dec 18 2011
G.f.: (28*x^2 + 34*x + 1)/(x-1)^4. - Harvey P. Dale, Dec 18 2011

A100169 Structured pentagonal hexacontahedral numbers (vertex structure 16).

Original entry on oeis.org

1, 92, 438, 1204, 2555, 4656, 7672, 11768, 17109, 23860, 32186, 42252, 54223, 68264, 84540, 103216, 124457, 148428, 175294, 205220, 238371, 274912, 315008, 358824, 406525, 458276, 514242, 574588, 639479, 709080, 783556, 863072
Offset: 1

Views

Author

James A. Record (james.record(AT)gmail.com), Nov 07 2004

Keywords

Links

Crossrefs

Cf. A100170 = alternate vertex; A100145 for more on structured numbers.

Programs

Formula

a(n) = (1/6)*(165*n^3 - 225*n^2 + 66*n).
G.f.: x*(1 + 88*x + 76*x^2)/(1-x)^4. - Colin Barker, Feb 14 2012
a(n) = (55*n^3 - 75*n^2 + 22*n)/2. - Wesley Ivan Hurt, Nov 26 2013

A100170 Structured pentagonal hexacontahedral numbers (vertex structure 10).

Original entry on oeis.org

1, 92, 444, 1228, 2615, 4776, 7882, 12104, 17613, 24580, 33176, 43572, 55939, 70448, 87270, 106576, 128537, 153324, 181108, 212060, 246351, 284152, 325634, 370968, 420325, 473876, 531792, 594244, 661403, 733440, 810526, 892832
Offset: 1

Views

Author

James A. Record (james.record(AT)gmail.com), Nov 07 2004

Keywords

Links

Crossrefs

Cf. A100169 = alternate vertex; A100145 for more on structured numbers.

Programs

Formula

a(n) = (1/6)*(171*n^3 - 243*n^2 + 78*n).
G.f.: x*(1 + 88*x + 82*x^2)/(1-x)^4. - Colin Barker, Feb 14 2012

A100172 Structured triakis icosahedral numbers (vertex structure 4).

Original entry on oeis.org

1, 32, 150, 412, 875, 1596, 2632, 4040, 5877, 8200, 11066, 14532, 18655, 23492, 29100, 35536, 42857, 51120, 60382, 70700, 82131, 94732, 108560, 123672, 140125, 157976, 177282, 198100, 220487, 244500, 270196, 297632
Offset: 1

Views

Author

James A. Record (james.record(AT)gmail.com), Nov 07 2004

Keywords

Links

Crossrefs

Cf. A100164 = alternate vertex; A100145 for more on structured numbers.

Programs

  • Magma
    [(1/6)*(57*n^3-81*n^2+30*n): n in [1..40]]; // Vincenzo Librandi, Jul 27 2011
  • Mathematica
    LinearRecurrence[{4,-6,4,-1},{1,32,150,412},50] (* Harvey P. Dale, Sep 18 2023 *)

Formula

a(n) = (1/6)*(57*n^3 - 81*n^2 + 30*n).
G.f.: x*(1 + 28*x + 28*x^2)/(1-x)^4. [Colin Barker, May 29 2012]

A100173 Structured pentakis dodecahedral numbers (vertex structure 6).

Original entry on oeis.org

1, 32, 148, 404, 855, 1556, 2562, 3928, 5709, 7960, 10736, 14092, 18083, 22764, 28190, 34416, 41497, 49488, 58444, 68420, 79471, 91652, 105018, 119624, 135525, 152776, 171432, 191548, 213179, 236380, 261206, 287712
Offset: 1

Views

Author

James A. Record (james.record(AT)gmail.com), Nov 07 2004

Keywords

Links

Crossrefs

Cf. A100165 = alternate vertex; A100145 for more on structured numbers.

Programs

  • Magma
    [(1/6)*(55*n^3-75*n^2+26*n): n in [1..40]]; // Vincenzo Librandi, Jul 26 2011
  • Mathematica
    LinearRecurrence[{4,-6,4,-1},{1,32,148,404},40] (* Harvey P. Dale, Aug 04 2022 *)

Formula

a(n) = (1/6)*(55*n^3 - 75*n^2 + 26*n).
G.f.: x*(1 + 28*x + 26*x^2)/(1-x)^4. - Colin Barker, May 29 2012
Previous Showing 51-60 of 63 results. Next

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