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.

A106470 Inverse of number triangle A106468.

Original entry on oeis.org

1, -1, 1, -1, 0, 1, 1, -1, -1, 1, 1, 0, -1, 0, 1, -1, 1, 1, -1, -1, 1, -1, 0, 1, 0, -1, 0, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 0, -1, 0, 1, 0, -1, 0, 1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, -1, 1, 1, -1, -1, 1, 1
Offset: 0

Views

Author

Paul Barry, May 03 2005

Keywords

Comments

A 'mixed' sequence array : rows alternate between the rows of the sequence array for the sequence 1,-1,-1,1,1,-1,-1,.. with g.f. (1-x)/(1+x^2) and the sequence array for the sequence 1,0,-1,0,-1,... with g.f. 1/(1+x^2). Column 2k has g.f. x^2k(1-x)/(1+x^2) column 2k+1 has g.f. x^(2k+1)/(1+x^2). Row sums are 1,0,0,0,1,0,0,0,1,.. with g.f. 1/(1-x^4).

Examples

			Triangle begins:
  1;
  -1, 1;
  -1, 0, 1;
  1, -1, -1, 1;
  1, 0, -1, 0, 1;
  -1, 1, 1, -1, -1, 1;
  ...

A106469 Expansion of (1 + x^2)*(1 + 2*x)/(1 - x^2).

Original entry on oeis.org

1, 2, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4
Offset: 0

Views

Author

Paul Barry, May 03 2005

Keywords

Links

Crossrefs

Row sums of A106468.

Programs

  • Mathematica
    CoefficientList[Series[(1+x^2)(1+2x)/(1-x^2),{x,0,95}],x] (* James C. McMahon, Feb 02 2024 *)

Formula

a(0)=1, a(n)=(2-0^((n-1)/2))(1-(-1)^n)+(2-0^(n/2))(1+(-1)^n)/2, n>1.
Showing 1-2 of 2 results.

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