A123918 - OEIS

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A123918

F(L(n)) - L(F(n)) where F(n) = n-th Fibonacci number and L(n) = n-th Lucas number. Commutator [Fibonacci,Lucas] at n.

-1, 0, 1, 0, 9, 78, 2537, 513708, 2971190597, 3416454610154664, 22698374052006551837970693, 173402521172797813159681057129399205126250 (list; graph; refs; listen; history; internal format)

	OFFSET	`0,5`
	COMMENTS	`a(0) = -1 is the only negative value. Asymptotic value left as an exercise for the reader.`
	FORMULA	`a(n) = A068096(n) - A068098(n). a(n) = Commutator [A000045,A000032] at n. a(n) = A000045(A000032(n)) - A000032(A000045(n)).`
	EXAMPLE	`a(0) = F(L(0)) - L(F(0)) = F(2) - L(0) = 1 - 2 = -1.` `a(1) = F(L(1)) - L(F(1)) = F(1) - L(1) = 1 - 1 = 0.` `a(2) = F(L(2)) - L(F(2)) = F(3) - L(1) = 2 - 1 = 1.` `a(3) = F(L(3)) - L(F(3)) = F(4) - L(2) = 3 - 3 = 0.` `a(4) = F(L(4)) - L(F(4)) = F(7) - L(3) = 13 - 4 = 9.` `a(5) = F(L(5)) - L(F(5)) = F(11) - L(5) = 89 - 11 = 78.` `a(6) = F(L(6)) - L(F(6)) = F(18) - L(8) = 2584 - 47 = 2537.` `a(7) = F(L(7)) - L(F(7)) = F(29) - L(13) = 514229 - 521 = 513708.` `a(8) = F(L(8)) - L(F(8)) = 2971215073 - 24476 = 2971190597.` `a(9) = F(L(9)) - L(F(9)) = 3416454622906707 - 12752043 = 3416454610154664.` `a(10) = F(L(10)) - L(F(10)) = 22698374052006863956975682 - 312119004989 = 22698374052006551837970693.` `a(11) = F(L(11)) - L(F(11)) = 173402521172797813159685037284371942044301 - 3980154972736918051 = 173402521172797813159681057129399205126250.`
	CROSSREFS	`Cf. A000032, A000045, A068096, A068098.` `Sequence in context: A000445 A046196 A190980 * A044577 A172203 A198857` `Adjacent sequences: A123915 A123916 A123917 * A123919 A123920 A123921`
	KEYWORD	`easy,sign`
	AUTHOR	`Jonathan Vos Post (jvospost3(AT)gmail.com), Oct 28 2006`

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Last modified February 16 15:27 EST 2012. Contains 205930 sequences.