A099147 Iterated hexagonal numbers, starting at 1.

1, 6, 66, 8646, 149497986, 44699295486614406, 3996054033999333969062944766851266, 31936895685284700329548847429175178142518023225832967407199564754246

Offset: 1

Author

Jonathan Vos Post, Nov 14 2004

Keywords

• nonn

Comments

Agrees with A097419 for n>1.

The next term (a(9)) has 136 digits. - Harvey P. Dale, Nov 24 2024

Examples

			a(4) = b(a(3)) = b(b(a(2))) = b(b(b(2))) = b(b(6)) = b(66) = 8646, where b(n) = A000384(n).
		

Links

• Eric Weisstein's World of Mathematics, Hexagonal Number.

Crossrefs

Cf. A000384, A097419.

Programs

Mathematica

Join[{1},NestList[PolygonalNumber[6,#]&,6,6]] (* Harvey P. Dale, Nov 24 2024 *)

PARI

{hexagonal(n) = n*(2*n-1)}
{a(n) = if(n<=2,hexagonal(n),hexagonal(a(n-1)))} \\ Klaus Brockhaus, Jan 10 2007

Formula

a(n) = b(n) for n<=2, a(n) = b(a(n-1)) for n>2, where b(n) = A000384(n) = n*(2*n-1), the hexagonal numbers.

a(1) = 1, a(2) = 6, a(n) = 2*a(n-1)^2 - a(n-1) for n>2.

Let H(n) = n*(2*n-1) = the n-th hexagonal number. Define A(n, k) recursively by A(1, k) = H(k), A(n, k) = A(1, A(n-1, k)) for n>1. Then a(1) = A(1, 1), a(n) = A(n-1, 2) for n>1.

Extensions

Edited by Klaus Brockhaus, Jan 10 2007