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A099147 Iterated hexagonal numbers, starting at 1. 4
1, 6, 66, 8646, 149497986, 44699295486614406, 3996054033999333969062944766851266, 31936895685284700329548847429175178142518023225832967407199564754246 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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.

Agrees with A097419 for n>1.

REFERENCES

J. V. Post, "Iterated Polygonal Numbers", preprint.

J. V. Post, "Iterated Triangular Numbers", preprint.

LINKS

Table of n, a(n) for n=1..8.

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

FORMULA

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.

EXAMPLE

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

PROG

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

CROSSREFS

Cf. A000384, A097419.

Sequence in context: A063039 A082781 A257049 * A073326 A024203 A231598

Adjacent sequences:  A099144 A099145 A099146 * A099148 A099149 A099150

KEYWORD

nonn

AUTHOR

Jonathan Vos Post, Nov 14 2004

EXTENSIONS

Edited by Klaus Brockhaus, Jan 10 2007

STATUS

approved

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Last modified November 21 01:33 EST 2019. Contains 329349 sequences. (Running on oeis4.)