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.

A216876 20k^2-20k-5 interleaved with 20k^2+5 for k=>0.

Original entry on oeis.org

-5, 5, -5, 25, 35, 85, 115, 185, 235, 325, 395, 505, 595, 725, 835, 985, 1115, 1285, 1435, 1625, 1795, 2005, 2195, 2425, 2635, 2885, 3115, 3385, 3635, 3925, 4195, 4505, 4795, 5125, 5435, 5785, 6115, 6485, 6835, 7225, 7595, 8005, 8395, 8825, 9235, 9685
Offset: 0

Views

Author

Eddie Gutierrez, Sep 18 2012

Keywords

Comments

The sequence (the second in the family) is present as a family of single interleaved sequence of which are separated or factored out of the larger sequence to give individual sequences. The larger sequence produces two smaller interleaved sequences where one of them has the formula above and a first interleaved sequence. There are a total of two sequences in this family.

Links

Crossrefs

Cf. A178218, A214345, A214493, A214393, A214405, A216871.

Programs

  • Magma
    &cat[[20*k^2-20*k-5, 20*k^2+5]: k in [0..22]]; // Bruno Berselli, Sep 27 2012
  • Mathematica
    Flatten[Table[{20*n^2 - 20*n - 5, 20*n^2 + 5}, {n, 0, 30}]] (* T. D. Noe, Sep 26 2012 *)
  • Maxima
    A216876(n):=(5/2)*(2*n*(n-2)-3*(-1)^n+1)$
makelist(A216876(n),n,0,30); /* Martin Ettl, Nov 01 2012 */
  • PARI
    vector(60,n,k=(n-1)\2;if(n%2,20*k^2-20*k-5,20*k^2+5)) \\ Charles R Greathouse IV, Sep 27 2012

Formula

Contribution from Bruno Berselli, Sep 27 2012: (Start)
G.f.: -5*(1-3*x+3*x^2-5*x^3)/((1+x)*(1-x)^3).
a(n) = (5/2)*(2*n*(n-2)-3*(-1)^n+1).
a(n) = 5*A214345(n-3) with A214345(-3)=-1, A214345(-2)=1, A214345(-1)=-1. (End)

Extensions

More terms from T. D. Noe, Sep 26 2012
Definition rewritten by Bruno Berselli, Oct 25 2012

A216852 18k^2-36k+9 interleaved with 18k^2-18k+9 for k>=0.

Original entry on oeis.org

9, 9, -9, 9, 9, 45, 63, 117, 153, 225, 279, 369, 441, 549, 639, 765, 873, 1017, 1143, 1305, 1449, 1629, 1791, 1989, 2169, 2385, 2583, 2817, 3033, 3285, 3519, 3789, 4041, 4329, 4599, 4905, 5193, 5517, 5823, 6165, 6489, 6849, 7191, 7569, 7929, 8325, 8703
Offset: 0

Views

Author

Eddie Gutierrez, Sep 17 2012

Keywords

Comments

The sequence is present as a family of single interleaved sequence of which there are many which are separated or factored out to give individual sequences. The larger sequence produces two smaller interleaved sequences where one of them has the formulas above and the other interleaved sequence has the formulas (18n^2-24n+1) and (18n^2-6n+5). The latter interleaved sequence is A214493. There are three sequences in this family.

Links

Crossrefs

Cf. A178218, A214345, A214393, A214405, A216844, A216865, A216875, A216876.

Programs

  • Magma
    &cat[[18*k^2-36*k+9, 18*k^2-18*k+9]: k in [0..23]]; // Bruno Berselli, Oct 01 2012
  • Mathematica
    Flatten[Table[{18 n^2 - 36 n + 9, 18 n^2 - 18 n + 9}, {n, 0, 23}]] (* Bruno Berselli, Oct 01 2012 *)
Flatten[Table[18n^2+9-{36n,18n},{n,0,50}]] (* or *) LinearRecurrence[ {2,0,-2,1},{9,9,-9,9},100] (* Harvey P. Dale, Apr 26 2014 *)
  • PARI
    vector(47, n, k=(n-1)\2; if(n%2, 18*k^2-36*k+9, 18*k^2-18*k+9)) \\ Bruno Berselli, Oct 01 2012

Formula

From Bruno Berselli, Oct 01 2012: (Start)
G.f.: 9*(1-x-3*x^2+5*x^3)/((1+x)*(1-x)^3).
a(n) = (9/4)*(2*n*(n-4)-3*(-1)^n+7).
a(n) = 9*A178218(n-3) with A178218(-3)=1, A178218(-2)=1, A178218(-1)=-1, A178218(0)=1. (End)
a(0)=9, a(1)=9, a(2)=-9, a(3)=9, a(n)=2*a(n-1)-2*a(n-3)+a(n-4). - Harvey P. Dale, Apr 26 2014

Extensions

Definition rewritten by Bruno Berselli, Oct 25 2012

A216853 18k^2-12k-7 interleaved with 18k^2+6k+5 for k>=0.

Original entry on oeis.org

-7, 5, -1, 29, 41, 89, 119, 185, 233, 317, 383, 485, 569, 689, 791, 929, 1049, 1205, 1343, 1517, 1673, 1865, 2039, 2249, 2441, 2669, 2879, 3125, 3353, 3617, 3863, 4145, 4409, 4709, 4991, 5309, 5609, 5945, 6263, 6617, 6953, 7325, 7679, 8069, 8441, 8849
Offset: 0

Views

Author

Eddie Gutierrez, Sep 17 2012

Keywords

Comments

The sequence (the third in the family) is present as a family of single interleaved sequence of which there are many which are separated or factored out to give individual sequences. The larger sequence produces two smaller interleaved sequences where one of them has the formulas above and the other interleaved sequence has the formulas (18n^2-24n-1) and (18n^2-6n+5). The latter interleaved sequence is A214493. There are three sequences in this family.

Links

Crossrefs

Cf. A178218, A214345, A214393, A214405, A216876.

Programs

  • Magma
    &cat[[18*k^2-12*k-7, 18*k^2+6*k+5]: k in [0..22]]; // Bruno Berselli, Oct 05 2012
  • Mathematica
    Flatten[Table[{18 n^2 - 12 n - 7, 18 n^2 + 6 n + 5}, {n, 0, 22}]] (* Bruno Berselli, Oct 05 2012 *)
  • PARI
    vector(46, n, k=(n-1)\2; if(n%2, 18*k^2-12*k-7, 18*k^2+6*k+5)) \\ Bruno Berselli, Oct 05 2012

Formula

G.f.: -(7-19*x+11*x^2-17*x^3)/((1+x)*(1-x)^3). - Bruno Berselli, Oct 05 2012
a(n) = (6*n*(3*n-4)-27*(-1)^n-1)/4. - Bruno Berselli, Oct 05 2012

Extensions

Definition rewritten by Bruno Berselli, Oct 25 2012
Showing 1-3 of 3 results.

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