1,2

A003101 is the ascending descending base exponent transform of natural numbers A000027. 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. The parity of this sequence cycles odd, even, odd, even, ... There is no nontrivial integer fixed point of the transform.

a(1) = 1. For n>1: a(n) = SUM[from i = 1 to n] (2n+1)^(2n-i).

a(2) = 4 because 1^3 + 3^1 = 1 + 3 = 4.

a(3) = 33 because 1^5 + 3^3 + 5^1 = 1 + 27 + 5 = 33.

a(4) = 406 because 1^7 + 3^5 + 5^3 + 7^1 = 1 + 243 + 125 + 7 = 376.

a(5) = 5665 because 1^9 + 3^7 + 5^5 + 7^3 + 9^1 = 5665.

a(6) = 115356 = 1^11 + 3^9 + 5^7 + 7^5 + 9^3 + 11^1.

a(7) = 3014209 = 1^13 + 3^11 + 5^9 + 7^7 + 9^5 + 11^3 + 13^1.

a(8) = 95722288 = 1^15 + 3^13 + 5^11 + 7^9 + 9^7 + 11^5 + 13^3 + 15^1.

a(9) = 3619661121 = 1^17 + 3^15 + 5^13 + 7^11 + 9^9 + 11^7 + 13^5 + 15^3 + 17^1.

a(10) = 161338248820 = 1^19 + 3^17 + 5^15 + 7^13 + 9^11 + 11^9 + 13^7 + 15^5 + 17^3 + 19^1.

Cf. A005408, A113122, A113153, A113154.

Sequence in context: A028576 A093185 A075132 this_sequence A156132 A111534 A162655

Adjacent sequences: A113167 A113168 A113169 this_sequence A113171 A113172 A113173

easy,nonn

Jonathan Vos Post (jvospost3(AT)gmail.com), Jan 06 2006