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A105225
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a(n+3) = 2a(n+2) - 3a(n+1) + 2a(n); a(0) = 1, a(1) = -1, a(2) = -2.
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1
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1, -1, -2, 1, 6, 5, -6, -15, -2, 29, 34, -23, -90, -43, 138, 225, -50, -499, -398, 601, 1398, 197, -2598, -2991, 2206, 8189, 3778, -12599, -20154, 5045, 45354, 35265, -55442, -125971, -15086, 236857, 267030, -206683, -740742, -327375, 1154110, 1808861, -499358, -4117079, -3118362, 5115797
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OFFSET
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0,3
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LINKS
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Table of n, a(n) for n=0..45.
Robert Munafo, Sequences Related to Floretions
Index entries for linear recurrences with constant coefficients, signature (2, -3, 2).
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FORMULA
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a(n) - a(n+1) = A002249(n).
a(n) = A002249(n+1) + 1)/2.
G.f.: -(3*x^2-3*x+1)/((x-1)*(2*x^2-x+1)). -- From Harvey P. Dale, Jul 23 2012
a(n)=1/2*(1+(1/2*(1-I*Sqrt[7]))^n+(1/2*(1+I*Sqrt[7]))^n) -- From Harvey P. Dale, Jul 23 2012
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MATHEMATICA
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LinearRecurrence[{2, -3, 2}, {1, -1, -2}, 50] (* or *) CoefficientList[ Series[ (-3*x^2+3*x-1)/(2*x^3-3*x^2+2*x-1), {x, 0, 50}], x] (* Harvey P. Dale, Jul 23 2012 *)
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PROG
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Floretion Algebra Multiplication Program, FAMP Code: 2tesseq[.5'j + .5'k + .5j' + .5k' + .5'ii' + .5e]
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CROSSREFS
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Cf. A002249, A014551.
Sequence in context: A331435 A159927 A176443 * A011018 A156993 A308431
Adjacent sequences: A105222 A105223 A105224 * A105226 A105227 A105228
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KEYWORD
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sign,easy
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AUTHOR
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Creighton Dement, Apr 14 2005
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STATUS
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approved
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