A113170 - OEIS

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A113170

Ascending descending base exponent transform of odd numbers A005408.

1, 4, 33, 376, 5665, 115356, 3014209, 95722288, 3619661121, 161338248820, 8349617508961, 493959321484584, 33041900704133473, 2479933070973253516 (list; graph; refs; listen; history; internal format)

	OFFSET	`1,2`
	COMMENTS	`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.`
	FORMULA	`a(1) = 1. For n>1: a(n) = SUM[from i = 1 to n] (2n+1)^(2n-i).`
	EXAMPLE	`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.`
	CROSSREFS	`Cf. A005408, A113122, A113153, A113154.` `Sequence in context: A093185 A198006 A075132 * A198900 A166906 A156132` `Adjacent sequences: A113167 A113168 A113169 * A113171 A113172 A113173`
	KEYWORD	`easy,nonn`
	AUTHOR	`Jonathan Vos Post (jvospost3(AT)gmail.com), Jan 06 2006`

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Last modified February 16 16:45 EST 2012. Contains 205938 sequences.