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A121621
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Real part of (2 + 3i)^n.
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2
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1, 2, -5, -46, -119, 122, 2035, 6554, -239, -86158, -341525, -246046, 3455641, 17021162, 23161315, -128629846, -815616479, -1590277918, 4241902555, 37641223154, 95420159401, -107655263398, -1671083125805, -5284814079046, 584824319281
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OFFSET
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0,2
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COMMENTS
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A121622 is the companion sequence generated from (3 + 2i).
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LINKS
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FORMULA
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Re(2 + 3i)^n = a(n) = 4*a(n-1) - 13*a(n-2).
G.f.: ( 1-2*x ) / ( 1 - 4*x + 13*x^2 ). - R. J. Mathar, Mar 03 2013
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EXAMPLE
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a(5) = 122 since (2 + 3i)^5 = (122 - 597i).
a(5) = 122 = 4*(-119) - 13*(-46) = 4*a(4) - 13*a(3).
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MAPLE
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A121621:=proc(n)global a:if(n=0)then a[0]:=1:elif(n=1)then a[1]:=2:else a[n]:=4*a[n-1]-13*a[n-2]:fi:return a[n]:end:
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MATHEMATICA
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CROSSREFS
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KEYWORD
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sign,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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