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A113170 Ascending descending base exponent transform of odd numbers A005408. 2
1, 4, 33, 376, 5665, 115356, 3014209, 95722288, 3619661121, 161338248820, 8349617508961, 493959321484584, 33041900704133473, 2479933070973253516, 207343189445230918785, 19175058576632809926496, 1949302342535131018462849, 216707770770991401785821668 (list; graph; refs; listen; history; text; 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.

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..295

FORMULA

a(1) = 1. For n>1: a(n) = Sum_{i=1..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.

MATHEMATICA

Table[Sum[(2 k + 1)^(2 n - 2 k + 1), {k, 1, n}], {n, 0, 10}] + 1 (* G. C. Greubel, May 18 2017 *)

PROG

(PARI) for(n=0, 25, print1(1 + sum(k=1, n, (2*k+1)^(2*n-2*k+1)), ", ")) \\ G. C. Greubel, May 18 2017

CROSSREFS

Cf. A005408, A113122, A113153, A113154.

Sequence in context: A075132 A303919 A208961 * A187738 A198900 A166906

Adjacent sequences:  A113167 A113168 A113169 * A113171 A113172 A113173

KEYWORD

easy,nonn

AUTHOR

Jonathan Vos Post, Jan 06 2006

STATUS

approved

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Last modified October 16 05:44 EDT 2018. Contains 316259 sequences. (Running on oeis4.)