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.

A260260 a(n) = n*(16*n^2 - 21*n + 7)/2.

Original entry on oeis.org

0, 1, 29, 132, 358, 755, 1371, 2254, 3452, 5013, 6985, 9416, 12354, 15847, 19943, 24690, 30136, 36329, 43317, 51148, 59870, 69531, 80179, 91862, 104628, 118525, 133601, 149904, 167482, 186383, 206655, 228346, 251504, 276177, 302413, 330260, 359766, 390979
Offset: 0

Views

Author

Bruno Berselli, Jul 21 2015

Keywords

Comments

Similar sequences, where P(s, m) = ((s-2)*m^2-(s-4)*m)/2 is the m-th s-gonal number:
A000578: P(3, m)*P( 3, m) - P(3, m-1)*P( 3, m-1);
A213772: P(3, m)*P( 4, m) - P(3, m-1)*P( 4, m-1) for m>0;
A005915: P(3, m)*P( 5, m) - P(3, m-1)*P( 5, m-1) " ;
A130748: P(3, m)*P( 6, m) - P(3, m-1)*P( 6, m-1) for m>1;
A027849: P(3, m)*P( 7, m) - P(3, m-1)*P( 7, m-1) for m>0;
A214092: P(3, m)*P( 8, m) - P(3, m-1)*P( 8, m-1) " ;
A100162: P(3, m)*P( 9, m) - P(3, m-1)*P( 9, m-1) " ;
A260260: P(3, m)*P(10, m) - P(3, m-1)*P(10, m-1), this sequence;
A100165: P(3, m)*P(11, m) - P(3, m-1)*P(11, m-1) for m>0.

Links

Crossrefs

Cf. A000217, A000292, A001107.
Subsequence of A047275.
Sequences of the same type (see comment): A000578, A005915, A027849, A100162, A100165, A130748, A213772, A214092.

Programs

  • Magma
    [n*(16*n^2-21*n+7)/2: n in [0..40]];
  • Mathematica
    Table[n (16 n^2 - 21 n + 7)/2, {n, 0, 40}]
LinearRecurrence[{4,-6,4,-1},{0,1,29,132},40] (* Harvey P. Dale, May 08 2025 *)
  • PARI
    vector(40, n, n--; n*(16*n^2-21*n+7)/2)
  • Sage
    [n*(16*n^2-21*n+7)/2 for n in (0..40)]

Formula

G.f.: x*(1 + 25*x + 22*x^2)/(1 - x)^4. [corrected by Georg Fischer, May 10 2019]
a(n) = A000217(n)*A001107(n) - A000217(n-1)*A001107(n-1), with A000217(-1) = 0.
a(n) = A000292(n) + 25*A000292(n-1) + 22*A000292(n-2), with A000292(-2) = A000292(-1) = 0.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n >= 4. - Wesley Ivan Hurt, Dec 18 2020
E.g.f.: exp(x)*x*(2 + 27*x + 16*x^2)/2. - Elmo R. Oliveira, Aug 08 2025

A100161 Structured disdyakis dodecahedral numbers (vertex structure 9).

Original entry on oeis.org

1, 26, 115, 308, 645, 1166, 1911, 2920, 4233, 5890, 7931, 10396, 13325, 16758, 20735, 25296, 30481, 36330, 42883, 50180, 58261, 67166, 76935, 87608, 99225, 111826, 125451, 140140, 155933, 172870, 190991, 210336
Offset: 1

Views

Author

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

Keywords

Comments

Also structured deltoidal icositetrahedral numbers (vertex structure 9) (cf. A100162 = alternate vertex).

Links

Crossrefs

Cf. A100162, A100163 = alternate vertices; A100145 for more on structured polyhedral numbers.

Programs

  • Magma
    [(1/6)*(40*n^3-48*n^2+14*n): n in [1..40]]; // Vincenzo Librandi, Jul 24 2011
  • Mathematica
    Table[(40n^3-48n^2+14n)/6,{n,40}] (* or *) LinearRecurrence[{4,-6,4,-1},{1,26,115,308},40] (* Harvey P. Dale, Sep 23 2016 *)

Formula

a(n) = (1/6)*(40*n^3 - 48*n^2 + 14*n).
G.f.: x*(1 + 22*x + 17*x^2)/(1-x)^4. - Colin Barker, Jan 19 2012

A100163 Structured disdyakis dodecahedral numbers (vertex structure 5).

Original entry on oeis.org

1, 26, 119, 324, 685, 1246, 2051, 3144, 4569, 6370, 8591, 11276, 14469, 18214, 22555, 27536, 33201, 39594, 46759, 54740, 63581, 73326, 84019, 95704, 108425, 122226, 137151, 153244, 170549, 189110, 208971, 230176
Offset: 1

Views

Author

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

Keywords

Links

Crossrefs

Cf. A100161, A100162 = alternate vertices; A100145 for more on structured polyhedral numbers.

Programs

  • Magma
    [(1/6)*(44*n^3-60*n^2+22*n): n in [1..40]]; // Vincenzo Librandi, Jul 25 2011

Formula

a(n) = (1/6)*(44*n^3 - 60*n^2 + 22*n).
G.f.: x*(1 + 22*x + 21*x^2)/(1-x)^4. - Colin Barker, Jan 19 2012
Showing 1-3 of 3 results.

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