A099147 - OEIS

%I #21 Nov 25 2024 12:18:54

%S 1,6,66,8646,149497986,44699295486614406,

%T 3996054033999333969062944766851266,

%U 31936895685284700329548847429175178142518023225832967407199564754246

%N Iterated hexagonal numbers, starting at 1.

%C Agrees with A097419 for n>1.

%C The next term (a(9)) has 136 digits. - _Harvey P. Dale_, Nov 24 2024

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HexagonalNumber.html">Hexagonal Number</a>.

%F 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.

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

%F 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.

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

%t Join[{1},NestList[PolygonalNumber[6,#]&,6,6]] (* _Harvey P. Dale_, Nov 24 2024 *)

%o (PARI)

%o {hexagonal(n) = n*(2*n-1)}

%o {a(n) = if(n<=2,hexagonal(n),hexagonal(a(n-1)))} \\ _Klaus Brockhaus_, Jan 10 2007

%Y Cf. A000384, A097419.

%K nonn,changed

%O 1,2

%A _Jonathan Vos Post_, Nov 14 2004

%E Edited by _Klaus Brockhaus_, Jan 10 2007