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A070370 a(n) = 5^n mod 16. 1
1, 5, 9, 13, 1, 5, 9, 13, 1, 5, 9, 13, 1, 5, 9, 13, 1, 5, 9, 13, 1, 5, 9, 13, 1, 5, 9, 13, 1, 5, 9, 13, 1, 5, 9, 13, 1, 5, 9, 13, 1, 5, 9, 13, 1, 5, 9, 13, 1, 5, 9, 13, 1, 5, 9, 13, 1, 5, 9, 13, 1, 5, 9, 13, 1, 5, 9, 13, 1, 5, 9, 13, 1, 5, 9, 13, 1, 5, 9, 13, 1, 5, 9, 13, 1, 5, 9, 13, 1, 5, 9, 13, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Period 4: repeat [1, 5, 9, 13].

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,0,0,1). [R. J. Mathar, Apr 20 2010]

FORMULA

a(n) = (1/6)*{25*(n mod 4)+[(n+1) mod 4]+[(n+2) mod 4]+[(n+3) mod 4]}. - Paolo P. Lava, Feb 24 2010

From R. J. Mathar, Apr 20 2010: (Start)

a(n) = a(n-4) for n>3.

G.f.: ( 1+5*x+9*x^2+13*x^3 ) / ( (1-x)*(1+x)*(1+x^2) ). (End)

a(n) = 7-2*((1+I)*(-I)^n+(1-I)*I^n+(-1)^n). - Bruno Berselli, Feb 07 2011

E.g.f.: 5*cosh(x) + 9*sinh(x) - 4*cos(x) - 4*sin(x). - G. C. Greubel, Mar 05 2016

a(n) = A130909(A000351(n)). - Michel Marcus, Jul 06 2016

MAPLE

seq(op([1, 5, 9, 13]), n=0..50); # Wesley Ivan Hurt, Jul 06 2016

MATHEMATICA

Table[Mod[5^n, 16], {n, 0, 100}] (* G. C. Greubel, Mar 05 2016 *)

PROG

(Sage) [power_mod(5, n, 16)for n in xrange(0, 93)] # Zerinvary Lajos, Nov 26 2009

(PARI) a(n) = lift(Mod(5, 16)^n); \\ Michel Marcus, Mar 05 2016

(MAGMA) &cat [[1, 5, 9, 13]^^30]; // Wesley Ivan Hurt, Jul 06 2016

CROSSREFS

Cf. A000351, A130909.

Sequence in context: A256604 A220187 A073853 * A277617 A103703 A143706

Adjacent sequences:  A070367 A070368 A070369 * A070371 A070372 A070373

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, May 12 2002

STATUS

approved

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Last modified November 22 09:35 EST 2017. Contains 295076 sequences.