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 1-3 of 3 results.

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]

A100160 Structured disdyakis triacontahedral numbers (vertex structure 5).

Original entry on oeis.org

1, 62, 299, 828, 1765, 3226, 5327, 8184, 11913, 16630, 22451, 29492, 37869, 47698, 59095, 72176, 87057, 103854, 122683, 143660, 166901, 192522, 220639, 251368, 284825, 321126, 360387, 402724, 448253, 497090, 549351, 605152
Offset: 1

Views

Author

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

Keywords

Links

Crossrefs

Cf. A100158, A100159 = alternate vertices; A100145 for more on structured polyhedral numbers.

Programs

  • Magma
    [(1/6)*(116*n^3-168*n^2+58*n): n in [1..40]]; // Vincenzo Librandi, Jul 19 2011

Formula

a(n) = (1/6)*(116*n^3 - 168*n^2 + 58*n).
G.f.: x*(1+x)*(1+57*x)/(1-x)^4. [Colin Barker, Apr 16 2012]

A100166 Structured deltoidal hexacontahedral numbers (vertex structure 9).

Original entry on oeis.org

1, 62, 295, 812, 1725, 3146, 5187, 7960, 11577, 16150, 21791, 28612, 36725, 46242, 57275, 69936, 84337, 100590, 118807, 139100, 161581, 186362, 213555, 243272, 275625, 310726, 348687, 389620, 433637, 480850, 531371, 585312
Offset: 1

Views

Author

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

Keywords

Links

Crossrefs

Cf. A100158, A100159 = alternate vertices; A100145 for more on structured numbers.

Programs

  • Magma
    [(1/6)*(112*n^3-156*n^2+50*n): n in [1..40]]; // Vincenzo Librandi, Jul 26 2011
  • Mathematica
    LinearRecurrence[{4,-6,4,-1},{1,62,295,812},40] (* Harvey P. Dale, Nov 15 2022 *)

Formula

a(n) = (1/6)*(112*n^3 - 156*n^2 + 50*n).
G.f.: x*(1 + 58*x + 53*x^2)/(1-x)^4. - Colin Barker, Jan 19 2012
Showing 1-3 of 3 results.

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

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