A060973 - OEIS

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A060973

a(2*n+1) = a(n+1)+a(n), a(2*n) = 2*a(n), with a(1)=0 and a(2)=1.

0, 1, 1, 2, 2, 2, 3, 4, 4, 4, 4, 4, 5, 6, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 10, 11, 12, 13, 14, 15, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32 (list; graph; refs; listen; history; internal format)

	OFFSET	`1,4`
	LINKS	`R. Stephan, Some divide-and-conquer sequences ...` `R. Stephan, Table of generating functions`
	FORMULA	`a(n) = n-A006165(n) = A006165(n)-A053646(n) = (n-A053646(n))/2 [for n>1 ]. If n = 22^m+k with 0< = k< = 2^m, then a(n) = 2^m; if n = 32^m+k with 0< = k< = 2^m, then a(n) = 2^m+k.` `G.f. -x/(1-x) + x/(1-x)^2 * (1 + sum(k>=0, t^2(t-1), t=x^2^k)). - Ralf Stephan (ralf(AT)ark.in-berlin.de), Sep 12 2003`
	EXAMPLE	`a(6)=2a(3)=21=2. a(7)=a(3)+a(4)=1+2=3.`
	MAPLE	`A060973 := proc(n) option remember; if n <= 2 then RETURN(n-1); fi; if n mod 2 = 0 then 2*A060973(n/2) else A060973((n-1)/2)+A060973((n+1)/2); fi; end;`
	CROSSREFS	`Sequence in context: A054225 A091822 A173022 * A097915 A029131 A162351` `Adjacent sequences: A060970 A060971 A060972 * A060974 A060975 A060976`
	KEYWORD	`nonn`
	AUTHOR	`Henry Bottomley (se16(AT)btinternet.com), May 09 2001`

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Last modified February 16 20:47 EST 2012. Contains 205965 sequences.