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

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

0,3

Links

Paolo Xausa, Table of n, a(n) for n = 0..10000

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

Example

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;
  ...

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]]

Crossrefs

Cf. A000108, A000217, A072643.

Row sums of A370221 (for n >= 1).

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

Sequence in context: A342511 A175520 A271668 * A072464 A262871 A160745

Adjacent sequences: A370288 A370289 A370290 * A370292 A370293 A370294

Keyword

nonn,easy,tabf

Author

Paolo Xausa, Feb 14 2024

Status

approved