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 1-4 of 4 results.

A171659 Lucas-version of A165293.

Original entry on oeis.org

2, 10, -2, 100, -30, 2, 1000, -400, 50, -2, 10000, -5000, 900, -70, 2, 100000, -60000, 14000, -1600, 90, -2
Offset: 1

Views

Author

Mark Dols, Dec 14 2009

Keywords

Examples

			Triangle begins:
2
10,-2
100,-30,2
1000,-400,50,-2

Crossrefs

Cf. A165293, A087799 (antidiagonal sums), A004189.

A168520 a(n) = 98*a(n-1) - a(n-2); a(1) = 0, a(2) = 10.

Original entry on oeis.org

0, 10, 980, 96030, 9409960, 922080050, 90354434940, 8853812544070, 867583274883920, 85014307126080090, 8330534515080964900, 816307368170808480110, 79989791546224150085880, 7838183264161795899936130, 768061970096309774043654860, 75262234886174196060378240150
Offset: 1

Views

Author

Mark Dols, Nov 28 2009

Keywords

Links

Crossrefs

Cf. A004189, A000108, A000984, A165293.

Programs

  • Magma
    I:=[0,10]; [n le 2 select I[n] else 98*Self(n-1)-Self(n-2): n in [1..40]]; // Vincenzo Librandi, Oct 13 2015
  • Mathematica
    LinearRecurrence[{98,-1},{0,10},30] (* Harvey P. Dale, Sep 19 2011 *)
CoefficientList[Series[10 x/(x^2 - 98 x + 1), {x, 0, 33}], x] (* Vincenzo Librandi, Oct 13 2015 *)
  • PARI
    concat(0, Vec(10*x^2/(x^2-98*x+1) + O(x^30))) \\ Colin Barker, Oct 08 2015

Formula

From Colin Barker, Oct 08 2015: (Start)
a(n) = 98*a(n-1) - a(n-2) for n>2.
O.g.f.: 10*x^2 / (x^2-98*x+1). (End)
E.g.f.: exp(49*x)*( (49/(2*sqrt(6)))*sinh(20*sqrt(6)*x) - 10*cosh(20*sqrt(6)*x) ) + 10. - G. C. Greubel, Jul 24 2016

Extensions

a(1)=1 changed to a(1)=10, and data changed accordingly, so sequence is a bisection of A004189- Mark Dols, Feb 01 2010
Changed name to match data and offset, Joerg Arndt, Oct 13 2015

A168522 a(n) = 98*a(n-1) - 2*a(n-2); a(1) = 0, a(2) = 1.

Original entry on oeis.org

0, 1, 98, 9602, 940800, 92179196, 9031679608, 884920243192, 86704120473600, 8495233965926416, 832359520419841568, 81554242533212620832, 7990651049213997158400, 782920694337905296281536, 76710246743016291041273728, 7516038339426920711452262272
Offset: 1

Views

Author

Mark Dols, Nov 28 2009

Keywords

Comments

a(n)/a(n+1) converges to 49 - sqrt(2399). - corrected by Mark Dols, Jun 20 2010

Links

Crossrefs

Cf. A168520, A004189, A000108, A000984, A165293

Programs

  • Magma
    [n le 2 select n-1 else 98*Self(n-1)-2*Self(n-2): n in [1..20]]; // Vincenzo Librandi, Jul 25 2016
  • Mathematica
    LinearRecurrence[{98,-2},{0,1}, 25] (* G. C. Greubel, Jul 25 2016 *)

Formula

G.f.: x^2/(1 - 98x + 2x^2). - Philippe Deléham, Nov 29 2009
E.g.f.: (1/(2*b))*exp(49*x)*( 49*sinh(b*x) - b*cosh(b*x) ) - (1/2), where b = sqrt(2399). - G. C. Greubel, Jul 25 2016

Extensions

Definition adapted to offset by Georg Fischer, Jun 19 2021

A178870 Signed Delannoy triangle convolved with 10^n.

Original entry on oeis.org

1, 10, -1, 100, -30, 1, 1000, -500, 50, -1, 10000, -7000, 1300, -70, 1, 100000, -90000, 25000, -2500, 90, -1, 1000000, -1100000, 410000, -63000, 4100, -110, 1, 10000000, -13000000, 6100000, -1290000, 129000, -6100, 130, -1
Offset: 0

Views

Author

Mark Dols, Jun 20 2010

Keywords

Comments

Row sums give A178869

Examples

			Triangle begins:
1
10, -1
100, -30, 1
1000, -500, 50, -1
10000, -7000, 1300, -70, 1
100000, -90000, 25000, -2500, 90, -1
1000000, -1100000, 410000, -63000, 4100, -110, 1
10000000, -13000000, 6100000, -1290000, 129000, -6100, 130, -1

Crossrefs

Cf. A008288, A165293, A178865, A178869

Formula

T(n,k) = A008288(n,k)*(-10)^(n-k)*(-1)^n, A008288 seen as a triangle read by rows. - Philippe Deléham, Feb 27 2013

Extensions

More terms from Philippe Deléham, Feb 27 2013
Showing 1-4 of 4 results.

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