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A180964 a(0)=1; for n>0, a(n)=1+3*A117571(n-1). 1
1, 4, 4, 10, 13, 13, 19, 22, 22, 28, 31, 31, 37, 40, 40, 46, 49, 49, 55, 58, 58, 64, 67, 67, 73, 76, 76, 82, 85, 85, 91, 94, 94, 100, 103, 103, 109, 112, 112, 118, 121, 121, 127, 130, 130, 136, 139, 139, 145, 148, 148, 154, 157, 157, 163, 166, 166, 172 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

B. Berselli, Table of n, a(n) for n = 0..10000.

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

FORMULA

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

a(n) = a(n-1) +a(n-3) -a(n-4) for n>3.

a(n) = (n-1)*(n mod 3) +(n+1)*(n+1 mod 3) +n*(n+2 mod 3).

a(n) = 3*n +sqrt(3)*cos((4*n-3)*pi/6) -sin((4*n-3)*pi/6).

a(n)-a(n-1) = 3*A080425(n+1) for n>0.

MATHEMATICA

CoefficientList[Series[(1 + 3 x + 5 x^3)/((1 - x)^2 (1 + x + x^2)), {x, 0, 60}], x] (* Vincenzo Librandi, Mar 26 2013 *)

LinearRecurrence[{1, 0, 1, -1}, {1, 4, 4, 10}, 60] (* Harvey P. Dale, Aug 05 2020 *)

PROG

(MAGMA) I:=[1, 4, 4, 10]; [n le 4 select I[n] else Self(n-1)+Self(n-3)-Self(n-4): n in [1..60]]; // Vincenzo Librandi, Mar 26 2013

CROSSREFS

Sequence in context: A279036 A182699 A058596 * A237668 A209423 A185784

Adjacent sequences:  A180961 A180962 A180963 * A180965 A180966 A180967

KEYWORD

nonn,easy

AUTHOR

Bruno Berselli, Sep 28 2010 - Oct 01 2010

STATUS

approved

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Last modified September 21 03:13 EDT 2020. Contains 337266 sequences. (Running on oeis4.)