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A083322 a(n) = 2^n - A081374(n). 3
1, 2, 6, 11, 22, 42, 85, 170, 342, 683, 1366, 2730, 5461, 10922, 21846, 43691, 87382, 174762, 349525, 699050, 1398102, 2796203, 5592406, 11184810, 22369621, 44739242, 89478486, 178956971, 357913942, 715827882, 1431655765, 2863311530, 5726623062 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (2,0,-1,2).

FORMULA

G.f. x*(1+2*x^2) / ( (1-2*x)*(1+x)*(1-x+x^2) ). - R. J. Mathar, May 27 2011

a(n)= 2*a(n-1) - a(n-3) + 2*a(n-4). - Paul Curtz, May 26 2011

a(n)+a(n+3) = 3*2^(n+1) = A007283(n+1). - Paul Curtz, May 27 2011

a(n+6)-a(n) = 21*2^(n+1) = A175805(n+1). - Paul Curtz, May 27 2011

MATHEMATICA

CoefficientList[Series[(1 + 2 x^2) / ((1 - 2 x) (1 + x) (1 - x + x^2)), {x, 0, 40}], x] (* Vincenzo Librandi, Jul 08 2016 *)

PROG

(MAGMA) I:=[1, 2, 6, 11]; [n le 4 select I[n] else 2*Self(n-1)-Self(n-3)+2*Self(n-4): n in [1..40]]; // Vincenzo Librandi, Jul 08 2016

CROSSREFS

Cf. A081374.

Sequence in context: A241564 A135348 A305101 * A073939 A085264 A005999

Adjacent sequences:  A083319 A083320 A083321 * A083323 A083324 A083325

KEYWORD

nonn

AUTHOR

David Applegate, Aug 22 2003

STATUS

approved

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Last modified November 15 22:20 EST 2018. Contains 317252 sequences. (Running on oeis4.)