id:A116590 - OEIS Search Results

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a(0)=1; a(n)=b(n+2)+b(n), where b(n)=A005185(n) is the Hofstadter Q-sequence: b(1)=b(2)=1; b(n)=b(n-b(n-1))+b(n-b(n-2)) for n > 2.

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1, 3, 4, 5, 7, 8, 9, 11, 11, 12, 14, 14, 16, 18, 17, 20, 20, 21, 23, 23, 24, 24, 28, 26, 30, 30, 30, 32, 32, 36, 33, 37, 37, 38, 39, 41, 41, 41, 44, 44, 45, 47, 47, 48, 48, 48, 56, 48, 57, 54, 53, 56, 58, 56, 58, 62, 58, 64, 62, 64, 64, 72, 65, 71, 71, 66, 71, 74, 73, 76, 78, 77 (list; graph; listen)

	OFFSET	`0,2`
	COMMENT	`A similar definition applied to the Fibonacci sequence (A000045) leads to the Lucas sequence (A000032).`
	FORMULA	`a(n)=A005185(n+2)+A005185(n) for n>=1.`
	MAPLE	`b:=proc(n) option remember; if n<=2 then 1 else b(n-b(n-1))+b(n-b(n-2)): fi: end: a[0]:=1: for n from 1 to 71 do a[n]:=b(n)+b(n+2) od: seq(a[n], n=0..71);`
	MATHEMATICA	`F[0] = 0; F[1] = 1; F[2] = 1; F[n_] := F[n] = F[n - F[n - 1]] + F[n - F[n - 2]] L[0] = 1; L[n_] := L[n] = F[n - 1] + F[n + 1] a = Table[L[n], {n, 1, 200}]`
	CROSSREFS	`Cf. A000030, A005185.` `Adjacent sequences: A116587 A116588 A116589 this_sequence A116591 A116592 A116593` `Sequence in context: A118170 A039094 A051374 this_sequence A024355 A137905 A074227`
	KEYWORD	`nonn`
	AUTHOR	`Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Mar 27 2006`
	EXTENSIONS	`Edited by njas, Apr 15 2006`

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Last modified October 13 20:18 EDT 2008. Contains 145016 sequences.

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