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 1-2 of 2 results.

A178977 a(n) = (3*n+2)*(3*n+5)/2.

Original entry on oeis.org

5, 20, 44, 77, 119, 170, 230, 299, 377, 464, 560, 665, 779, 902, 1034, 1175, 1325, 1484, 1652, 1829, 2015, 2210, 2414, 2627, 2849, 3080, 3320, 3569, 3827, 4094, 4370, 4655, 4949, 5252, 5564, 5885, 6215, 6554, 6902, 7259, 7625, 8000, 8384, 8777, 9179, 9590, 10010
Offset: 0

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Author

Paul Curtz, Jan 02 2011

Keywords

Comments

Companion to A145910.

Links

Crossrefs

Cf. A008585, A145910, A168233, A168300, A016789, A178971, A235332.

Programs

Formula

a(n) = a(n-1) + 6 + 9*n.
a(n) = A178971(3*n+2).
a(n) = A145910(n) + 3 + 3*n = A145910(n) + A008585(n+1).
a(n) = A168233(n+1)*A168300(n+1).
G.f.: (-5-5*x+x^2)/(x-1)^3. [Adapted to the offset by Bruno Berselli, Apr 14 2011]
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Harvey P. Dale, Apr 19 2013
From Amiram Eldar, Mar 10 2022: (Start)
Sum_{n>=0} 1/a(n) = 1/3.
Sum_{n>=0} (-1)^n/a(n) = 4*Pi/(9*sqrt(3)) - 1/3 - 4*log(2)/9. (End)
From Elmo R. Oliveira, Oct 30 2024: (Start)
E.g.f.: exp(x)*exp(x)*(5 + 15*x + 9*x^2/2).
a(n) = A016789(n)*A016789(n+1)/2. (End)

A168326 a(n) = (6*n - 3*(-1)^n - 1)/2.

Original entry on oeis.org

4, 4, 10, 10, 16, 16, 22, 22, 28, 28, 34, 34, 40, 40, 46, 46, 52, 52, 58, 58, 64, 64, 70, 70, 76, 76, 82, 82, 88, 88, 94, 94, 100, 100, 106, 106, 112, 112, 118, 118, 124, 124, 130, 130, 136, 136, 142, 142, 148, 148, 154, 154, 160, 160, 166, 166, 172, 172, 178, 178
Offset: 1

Views

Author

Vincenzo Librandi, Nov 23 2009

Keywords

Links

Crossrefs

Cf. A016957, A168236.

Programs

  • Magma
    [n eq 1 select n+3 else 6*n-Self(n-1)-4: n in [1..70]]; // Vincenzo Librandi, Sep 17 2013
  • Mathematica
    With[{c = 6 Range[0, 30] + 4}, Riffle[c, c]] (* or *) RecurrenceTable[ {a[1] == 4, a[n] == 6 n - a[n-1] - 4}, a, {n, 60}] (* Harvey P. Dale, Jun 12 2012 *)
Table[3 n - 3 (-1)^n/2 - 1/2, {n, 70}] (* Bruno Berselli, Sep 17 2013 *)
CoefficientList[Series[(4 + 2 x^2) / ((1 + x) (1 - x)^2), {x, 0, 70}], x] (* Vincenzo Librandi, Sep 17 2013 *)

Formula

a(n) = 6*n - a(n-1) - 4, with n>1, a(1)=4.
From Vincenzo Librandi, Sep 17 2013: (Start)
G.f.: 2*x*(2 + x^2)/((1+x)*(1-x)^2).
a(n) = 2*A168236(n) = A168300(n) - 1 = A168329(n) + 1 = A168301(n+1) - 3.
a(n) = a(n-1) +a(n-2) -a(n-3). (End)
E.g.f.: (1/2)*(-3 + 4*exp(x) + (6*x - 1)*exp(2*x))*exp(-x). - G. C. Greubel, Jul 18 2016

Extensions

New definition by Bruno Berselli, Sep 17 2013
Showing 1-2 of 2 results.

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