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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A100159 Structured disdyakis triacontahedral numbers (vertex structure 7).

Original entry on oeis.org

1, 62, 297, 820, 1745, 3186, 5257, 8072, 11745, 16390, 22121, 29052, 37297, 46970, 58185, 71056, 85697, 102222, 120745, 141380, 164241, 189442, 217097, 247320, 280225, 315926, 354537, 396172, 440945, 488970, 540361, 595232
Offset: 1

Views

Author

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

Keywords

Comments

Also structured deltoidal hexacontahedral numbers (vertex structure 7) (cf. A100158, A100166 = alternate vertices).

Links

Crossrefs

Cf. A100158, A100160 = alternate vertices; A100145 for more on structured polyhedral numbers.

Programs

  • Magma
    [(1/6)*(114*n^3-162*n^2+54*n): n in [1..40]]; // Vincenzo Librandi, Jul 19 2011

Formula

a(n) = (1/6)*(114*n^3 - 162*n^2 + 54*n) = n*(19*n^2 - 27*n + 9).
G.f.: x*(1 + 58*x + 55*x^2)/(1-x)^4. [Colin Barker, Apr 16 2012]

A100162 Structured disdyakis dodecahedral numbers (vertex structure 7).

Original entry on oeis.org

1, 26, 117, 316, 665, 1206, 1981, 3032, 4401, 6130, 8261, 10836, 13897, 17486, 21645, 26416, 31841, 37962, 44821, 52460, 60921, 70246, 80477, 91656, 103825, 117026, 131301, 146692, 163241, 180990, 199981, 220256
Offset: 1

Views

Author

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

Keywords

Comments

Also structured deltoidal icositetrahedral numbers (vertex structure 7) (cf. A100161 = alternate vertex).

Links

Crossrefs

Cf. A100161, A100163 = alternate vertices; A100145 for more on structured polyhedral numbers.
Cf. A260260 (comment). - Bruno Berselli, Jul 22 2015

Programs

  • Magma
    [(1/6)*(42*n^3-54*n^2+18*n): n in [1..40]]; // Vincenzo Librandi, Jul 24 2011

Formula

a(n) = (1/6)*(42*n^3 - 54*n^2 + 18*n).
G.f.: x*(1 + 22*x + 19*x^2)/(1-x)^4. - Colin Barker, Jan 19 2012

A100146 Structured great rhombicubeoctahedral numbers.

Original entry on oeis.org

1, 48, 221, 600, 1265, 2296, 3773, 5776, 8385, 11680, 15741, 20648, 26481, 33320, 41245, 50336, 60673, 72336, 85405, 99960, 116081, 133848, 153341, 174640, 197825, 222976, 250173, 279496, 311025, 344840, 381021, 419648, 460801, 504560, 551005, 600216, 652273
Offset: 1

Views

Author

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

Keywords

Links

Crossrefs

Cf. A100145, A100147 for adjacent structured Archimedean solids; and A100145 for more on structured polyhedral numbers.

Programs

  • Magma
    [((n-1)+1)*(5*(n-1)+3)*(8*(n-1)+1)/3: n in [1..40]]; // Vincenzo Librandi, Jul 19 2011

Formula

a(n) = (1/6)*(80*n^3 - 102*n^2 + 28*n).
From Jaume Oliver Lafont, Sep 08 2009: (Start)
a(n) = ((n-1)+1)*(5*(n-1)+3)*(8*(n-1)+1)/3.
G.f.: x*(1 + 44*x + 35*x^2)/(1-x)^4. (End)
From Elmo R. Oliveira, Aug 05 2025: (Start)
E.g.f.: exp(x)*x*(40*x^2 + 69*x + 3)/3.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n > 4. (End)

A100148 Structured small rhombicosidodecahedral numbers.

Original entry on oeis.org

1, 60, 285, 784, 1665, 3036, 5005, 7680, 11169, 15580, 21021, 27600, 35425, 44604, 55245, 67456, 81345, 97020, 114589, 134160, 155841, 179740, 205965, 234624, 265825, 299676, 336285, 375760, 418209, 463740, 512461, 564480
Offset: 1

Views

Author

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

Keywords

Links

Crossrefs

Cf. A100147, A100149 for adjacent structured Archimedean solids; and A100145 for more on structured polyhedral numbers.

Programs

  • Magma
    [(1/6)*(108*n^3-150*n^2+48*n): n in [1..40]]; // Vincenzo Librandi, Jul 19 2011
  • Mathematica
    Table[(108n^3-150n^2+48n)/6,{n,40}] (* or *) LinearRecurrence[ {4,-6,4,-1},{1,60,285,784},40](* Harvey P. Dale, Oct 10 2011 *)
  • PARI
    vector(50, n, (108*n^3 - 150*n^2 + 48*n)/6) \\ G. C. Greubel, Oct 18 2018

Formula

a(n) = (1/6)*(108*n^3 - 150*n^2 + 48*n).
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4); a(1)=1, a(2)=60, a(3)=285, a(4)=784. - Harvey P. Dale, Oct 10 2011
G.f.: x*(x*(51*x+56)+1)/(x-1)^4. - Harvey P. Dale, Oct 10 2011
E.g.f.: x*(1 + 29*x + 18*x^2)*exp(x). - G. C. Greubel, Oct 18 2018

A100149 Structured small rhombicubeoctahedral numbers.

Original entry on oeis.org

1, 24, 106, 284, 595, 1076, 1764, 2696, 3909, 5440, 7326, 9604, 12311, 15484, 19160, 23376, 28169, 33576, 39634, 46380, 53851, 62084, 71116, 80984, 91725, 103376, 115974, 129556, 144159, 159820, 176576, 194464, 213521, 233784, 255290, 278076, 302179, 327636
Offset: 1

Views

Author

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

Keywords

Links

Crossrefs

Cf. A100148, A100150 for adjacent structured Archimedean solids; and A100145 for more on structured polyhedral numbers.

Programs

  • Magma
    [(1/6)*(37*n^3-45*n^2+14*n): n in [1..40]]; // Vincenzo Librandi, Jul 19 2011

Formula

a(n) = (1/6)*(37*n^3 - 45*n^2 + 14*n).
G.f.: x*(1 + 20*x + 16*x^2)/(1-x)^4. - Colin Barker, Jan 19 2012
From Elmo R. Oliveira, Aug 05 2025: (Start)
E.g.f.: exp(x)*x*(37*x^2 + 66*x + 6)/6.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n > 4. (End)

A100150 Structured snub cubic numbers.

Original entry on oeis.org

1, 24, 107, 288, 605, 1096, 1799, 2752, 3993, 5560, 7491, 9824, 12597, 15848, 19615, 23936, 28849, 34392, 40603, 47520, 55181, 63624, 72887, 83008, 94025, 105976, 118899, 132832, 147813, 163880, 181071, 199424, 218977, 239768, 261835, 285216, 309949, 336072
Offset: 1

Views

Author

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

Keywords

Links

Crossrefs

Cf. A100149, A100151 for adjacent structured Archimedean solids; and A100145 for more on structured polyhedral numbers.

Programs

Formula

a(n) = (1/6)*(38*n^3 - 48*n^2 + 16*n).
G.f.: x*(1 + 20*x + 17*x^2)/(1-x)^4. - Colin Barker, Jan 19 2012
From Elmo R. Oliveira, Aug 05 2025: (Start)
E.g.f.: exp(x)*x*(19*x^2 + 33*x + 3)/3.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n > 4. (End)

Extensions

Deleted extra +16 in formula, corrected by Craig Ferguson, Jul 18 2011

A100151 Structured snub dodecahedral numbers.

Original entry on oeis.org

1, 60, 286, 788, 1675, 3056, 5040, 7736, 11253, 15700, 21186, 27820, 35711, 44968, 55700, 68016, 82025, 97836, 115558, 135300, 157171, 181280, 207736, 236648, 268125, 302276, 339210, 379036, 421863, 467800, 516956, 569440, 625361, 684828, 747950, 814836, 885595
Offset: 1

Views

Author

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

Keywords

Links

Crossrefs

Cf. A100150, A100152 for adjacent structured Archimedean solids; and A100145 for more on structured polyhedral numbers.

Programs

  • Magma
    [(1/6)*(109*n^3-153*n^2+50*n): n in [1..40]]; // Vincenzo Librandi, Jul 19 2011
  • Mathematica
    LinearRecurrence[{4, -6, 4, -1}, {1, 60, 286, 788}, 50] (* Paolo Xausa, Aug 06 2025 *)

Formula

a(n) = (1/6)*n*(109*n^2 - 153*n + 50).
G.f.: x*(1 + 56*x + 52*x^2)/(1-x)^4. - Colin Barker, Jan 19 2012
From Elmo R. Oliveira, Aug 05 2025: (Start)
E.g.f.: exp(x)*x*(109*x^2 + 174*x + 6)/6.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n > 4. (End)

A100152 Structured truncated cubic numbers.

Original entry on oeis.org

1, 24, 100, 260, 535, 956, 1554, 2360, 3405, 4720, 6336, 8284, 10595, 13300, 16430, 20016, 24089, 28680, 33820, 39540, 45871, 52844, 60490, 68840, 77925, 87776, 98424, 109900, 122235, 135460, 149606, 164704
Offset: 1

Views

Author

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

Keywords

Links

Crossrefs

Cf. A100151, A100153 for adjacent structured Archimedean solids; A100145 for more on structured polyhedral numbers. Similar to truncated cubic numbers A005912.

Programs

  • Magma
    [(1/6)*(31*n^3-27*n^2+2*n): n in [1..40]]; // Vincenzo Librandi, Jul 19 2011
  • Mathematica
    Table[n/6 (31n^2-27n+2),{n,40}] (* or *) LinearRecurrence[{4,-6,4,-1},{1,24,100,260},40] (* Harvey P. Dale, Jan 11 2016 *)
  • PARI
    vector(50, n, (31*n^3-27*n^2+2*n)/6) \\ G. C. Greubel, Oct 18 2018

Formula

a(n) = (1/6)*n*(31*n^2 - 27*n + 2).
G.f.: x*(1 + 20*x + 10*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)=24, a(3)=100, a(4)=260. - Harvey P. Dale, Jan 11 2016
E.g.f.: x*(6 + 66*x + 31*x^2)*exp(x)/6. - G. C. Greubel, Oct 18 2018

A100153 Structured truncated dodecahedral numbers.

Original entry on oeis.org

1, 60, 276, 748, 1575, 2856, 4690, 7176, 10413, 14500, 19536, 25620, 32851, 41328, 51150, 62416, 75225, 89676, 105868, 123900, 143871, 165880, 190026, 216408, 245125, 276276, 309960, 346276, 385323, 427200, 472006, 519840
Offset: 1

Views

Author

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

Keywords

Links

Crossrefs

Cf. A100152, A100154 for adjacent structured Archimedean solids; A100145 for more on structured polyhedral numbers.

Programs

  • Magma
    [(1/6)*(99*n^3-123*n^2+30*n): n in [1..40]]; // Vincenzo Librandi, Jul 19 2011
  • Maple
    A100153:=n->(n*(33*n^2-41*n+10))/2; seq(A100153(k), k=1..40); # Wesley Ivan Hurt, Oct 24 2013
  • Mathematica
    Table[(n(33n^2-41n+10))/2,{n,40}] (* or *) LinearRecurrence[{4,-6,4,-1},{1,60,276,748},40] (* Harvey P. Dale, Dec 09 2012 *)
  • PARI
    vector(50, n, n*(33*n^2 - 41*n + 10)/2) \\ G. C. Greubel, Oct 18 2018

Formula

a(n) = (1/2)*n*(33*n^2 - 41*n + 10).
G.f.: x*(1 + 56*x + 42*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)=60, a(3)=276, a(4)=748. - Harvey P. Dale, Dec 09 2012
E.g.f.: x*(2 + 58*x + 33*x^2)*exp(x)/2. - G. C. Greubel, Oct 18 2018

A100154 Structured truncated icosahedral numbers.

Original entry on oeis.org

1, 60, 282, 772, 1635, 2976, 4900, 7512, 10917, 15220, 20526, 26940, 34567, 43512, 53880, 65776, 79305, 94572, 111682, 130740, 151851, 175120, 200652, 228552, 258925, 291876, 327510, 365932, 407247, 451560, 498976, 549600, 603537, 660892, 721770, 786276, 854515
Offset: 1

Views

Author

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

Keywords

Links

Crossrefs

Cf. A100153, A100155 for adjacent structured Archimedean solids; A100145 for more on structured polyhedral numbers.

Programs

  • Magma
    [(1/6)*(105*n^3-141*n^2+42*n): n in [1..40]]; // Vincenzo Librandi, Jul 19 2011
  • Mathematica
    LinearRecurrence[{4, -6, 4, -1},{1, 60, 282, 772}, 50] (* Paolo Xausa, Aug 06 2025 *)

Formula

a(n) = (1/2)*n*(35*n^2 - 47*n + 14).
G.f.: x*(1 + 56*x + 48*x^2)/(1-x)^4. - Colin Barker, Feb 12 2012
From Elmo R. Oliveira, Aug 05 2025: (Start)
E.g.f.: exp(x)*x*(35*x^2 + 58*x + 2)/2.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n > 4. (End)
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