id:A105309 - OEIS Search Results

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a(n) = |b(n)|^2 = x^2 + 3*y*2 where (x,y,y,y) is the quaternion b(n) of the sequence b of quaternions defined by b(0)=1,b(1)=1, b(n) = b(n-1) + b(n-2)*(0,c,c,c) where c = 1/sqrt(3).

+0
3

1, 1, 2, 5, 9, 20, 41, 85, 178, 369, 769, 1600, 3329, 6929, 14418, 30005, 62441, 129940, 270409, 562725, 1171042, 2436961, 5071361, 10553600, 21962241, 45703841, 95110562, 197926885, 411889609, 857150100, 1783745641, 3712008565 (list; graph; listen)

	OFFSET	`0,3`
	LINKS	`Eric Weisstein. "Quaternion"`
	FORMULA	`a(n) = A092886(n+1)-A092886(n-1), n>0.`
	PROGRAM	`(PARI) {a(n)=local(A); if(n<2, n>=0, n++; A=vector(n, i, 1); for(i=3, n, A[i]=A[i-1]+A[i-2]*I); norm(A[n]))} (Somos)`
	CROSSREFS	`Sequence in context: A062092 A079117 A030137 this_sequence A097163 A117186 A001851` `Adjacent sequences: A105306 A105307 A105308 this_sequence A105310 A105311 A105312`
	KEYWORD	`nonn`
	AUTHOR	`Gerald McGarvey (gerald.mcgarvey(AT)comcast.net), Apr 25 2005`

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Last modified July 24 12:00 EDT 2008. Contains 142294 sequences.

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