A113208 Half-fixed-point of ascending descending base exponent transform.

1, 1, 2, 4, 10, 44, 1426, 17592187106356

Offset

1,3

Comments

a(9) has 429 digits.

The ascending descending base exponent transform applied to the Fibonacci numbers is A113122; applied to the tribonacci numbers is A113153; applied to the Lucas numbers is A113154. There is no nontrivial integer fixed point of the transform.

Links

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

Formula

a(1) = 1. For n > 1: a(n) = (1/2) * Sum_{i=1..n} a(i)^a(n-i+1).

Example

a(2) = 1 because a(1)^a(2) + a(2)^a(1) = 1^1 + 1^1 = 2 and 2/2 = 1.
a(3) = 2 because a(1)^a(3) + a(2)^a(2) + a(3)^a(1) = 1^2 + 1^1 + 2^1 = 4 and 4/2 = 2.
a(4) = 4 because a(1)^a(4) + a(2)^a(3) + a(3)^a(2) + a(4)^a(1) = 1^4 + 1^2 + 2^1 + 4^1 = 8 and 8/2 = 4.
a(5) = 10 because a(1)^a(5) + a(2)^a(4) + a(3)^a(3) + a(4)^a(2) + a(5)^a(1) = 1^10 + 1^4 + 2^2 + 4^1 + 10^1 = 20 and 20/2 = 10.
a(6) = 44 because 1^44 + 1^10 + 2^4 + 4^2 + 10^1 + 44^1 = 88 and 88/2 = 44.
a(7) = (1^1426 + 1^44 + 2^10 + 4^4 + 10^2 + 44^1 + 1426^1)/2 = 1426.
a(8) = (1^17592187106356 + 1^1426 + 2^44 + 4^10 + 10^4 + 44^2 + 1426^1 + 17592187106356^1)/2 = 17592187106356.

Crossrefs

Cf. A113122, A113153, A113154.

Sequence in context: A125805 A344790 A028404 * A173488 A000613 A322294

Adjacent sequences: A113205 A113206 A113207 * A113209 A113210 A113211

Keyword

easy,nonn

Author

Jonathan Vos Post, Jan 06 2006

Status

approved