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 A121621 Real part of (2 + 3i)^n. 2
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS A121622 is the companion sequence generated from (3 + 2i). LINKS Nathaniel Johnston, Table of n, a(n) for n = 0..500 Index entries for linear recurrences with constant coefficients, signature (4,-13) FORMULA 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 EXAMPLE a(5) = 122 since (2 + 3i)^5 = (122 - 597i). a(5) = 122 = 4*(-119) - 13*(-46) = 4*a(4) - 13*a(3). MAPLE 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: seq(A121621(n), n=0..20); ## Nathaniel Johnston, Apr 15 2011 MATHEMATICA f[n_] := Re[(2 + 3I)^n]; Table[f[n], {n, 0, 24}] (* Robert G. Wilson v *) CROSSREFS Cf. A121622. Sequence in context: A088309 A056680 A005166 * A225147 A119715 A023273 Adjacent sequences:  A121618 A121619 A121620 * A121622 A121623 A121624 KEYWORD sign,easy AUTHOR Gary W. Adamson and Nick Williams, Aug 10 2006 EXTENSIONS More terms from Robert G. Wilson v, Aug 17 2006 STATUS approved

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