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.

A370291 Triangular number T(n) = A000217(n) occurs C(n) = A000108(n) times.

Original entry on oeis.org

0, 1, 3, 3, 6, 6, 6, 6, 6, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 21, 21, 21, 21, 21
Offset: 0

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Author

Paolo Xausa, Feb 14 2024

Keywords

Examples

			Written as a triangle:
   0;
   1;
   3,  3;
   6,  6,  6,  6,  6;
  10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10;
  ...
		

Crossrefs

Row sums of A370221 (for n >= 1).
Row sums as triangle give A002457(n-1) for n>=1.

Programs

  • Maple
    T:= n-> n*(n+1)/2$binomial(2*n,n)/(n+1):
    seq(T(n), n=0..5);  # Alois P. Heinz, Feb 16 2024
  • Mathematica
    Flatten[Array[Table[PolygonalNumber[#], CatalanNumber[#]] &, 7, 0]]

Formula

a(n) = A000217(A072643(n)).
Sum_{n>=1} (-1)^(n+1)/a(n) = Sum_{n>=1} (-1/2)^(n-1)/(2^n-1) = 0.86233289403022175171... . - Amiram Eldar, Feb 17 2024