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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 to sequences with 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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Last modified October 21 04:59 EDT 2014. Contains 248373 sequences.