A166473 - OEIS

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A166473

a(n) = 2^L(n+1) * 3^L(n)/12, where L(n) is the n-th Lucas number (A000032(n)).

2, 36, 864, 373248, 3869835264, 17332899271409664, 804905577934332296851095552, 167416167663978753511691999938432197602574336 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`1,1`
	COMMENTS	`For m>1, A166469(A002110(m)*a(n)) = L(m+n).` `A166469(a(n)) = L(n+2) - 2 = A014739(n).`
	LINKS	`G. C. Greubel, Table of n, a(n) for n = 1..14`
	FORMULA	`a(n) = A166471(n)/12.` `For n>1, a(n) = 12a(n-1) a(n-2).`
	MATHEMATICA	`Table[(2^LucasL[n+1] 3^LucasL[n])/12, {n, 10}] (* Harvey P. Dale, Aug 17 2011 *)`
	PROG	`(PARI) lucas(n) = fibonacci(n+1) + fibonacci(n-1);` `vector(10, n, 2^(lucas(n+1)-2)3^(lucas(n)-1) ) \\ G. C. Greubel, Jul 22 2019` `(MAGMA) [2^(Lucas(n+1)-2)3^(Lucas(n)-1): n in [1..10]]; // G. C. Greubel, Jul 22 2019` `(Sage) [2^(lucas_number2(n+1, 1, -1)-2)3^(lucas_number2(n, 1, -1)-1) for n in (1..10)] # G. C. Greubel, Jul 22 2019` `(GAP) List([1..10], n-> 2^(Lucas(1, -1, n+1)[2]-2)3^(Lucas(1, -1, n)[2]-1)); # G. C. Greubel, Jul 22 2019`
	CROSSREFS	`Subsequence of A003586, A025487.` `Sequence in context: A336714 A093530 A001626 * A279575 A009539 A009554` `Adjacent sequences: A166470 A166471 A166472 * A166474 A166475 A166476`
	KEYWORD	`nonn`
	AUTHOR	`Matthew Vandermast, Nov 05 2009`
	STATUS	`approved`

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Last modified March 2 19:18 EST 2021. Contains 341756 sequences. (Running on oeis4.)