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A168282 (10*n + 5*(-1)^n - 1)/4. 4
1, 6, 6, 11, 11, 16, 16, 21, 21, 26, 26, 31, 31, 36, 36, 41, 41, 46, 46, 51, 51, 56, 56, 61, 61, 66, 66, 71, 71, 76, 76, 81, 81, 86, 86, 91, 91, 96, 96, 101, 101, 106, 106, 111, 111, 116, 116, 121, 121, 126, 126, 131, 131, 136, 136, 141, 141, 146, 146, 151, 151, 156 (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 (1,1,-1).

FORMULA

a(n) = 5*n - a(n-1) - 3 for n>1, a(1)=1.

a(1)=1, a(2)=6, a(3)=6; for n>3, a(n) = a(n-1) +a(n-2) -a(n-3). - Harvey P. Dale, Jun 17 2013

From Bruno Berselli, Sep 16 2013: (Start)

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

a(n) = A168457(n)/2.

a(n) = A168278(n) - 1.

a(n) = ( A168459(n) + 1 )/2. (End)

E.g.f.: (1/4)*(5 - 4*exp(x) + (2*x - 1)*exp(2*x))*exp(-x). - G. C. Greubel, Jul 16 2016

MATHEMATICA

RecurrenceTable[{a[1]==1, a[n]==5n-a[n-1]-3}, a, {n, 70}] (* or *) LinearRecurrence[{1, 1, -1}, {1, 6, 6}, 70] (* Harvey P. Dale, Jun 17 2013 *)

Table[5 n/2 + 5 (-1)^n/4 - 1/4, {n, 70}] (* Bruno Berselli, Sep 16 2013 *)

CoefficientList[Series[(1 + 5 x - x^2) / ((1 + x) (1 - x)^2), {x, 0, 70}], x] (* Vincenzo Librandi, Sep 16 2013 *)

PROG

(MAGMA) [n le 1 select (n) else 5*n-Self(n-1)-3: n in [1..70]]; // Vincenzo Librandi, Sep 16 2013

(PARI) a(n)=5*n/2+5*(-1)^n/4-1/4 \\ Charles R Greathouse IV, Oct 16 2015

CROSSREFS

Cf. A016861, A168278, A168457, A168459.

Sequence in context: A220439 A240620 A344328 * A122762 A046605 A095899

Adjacent sequences:  A168279 A168280 A168281 * A168283 A168284 A168285

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Nov 22 2009

EXTENSIONS

New definition by Bruno Berselli, Sep 16 2013

STATUS

approved

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Last modified September 19 18:36 EDT 2021. Contains 347564 sequences. (Running on oeis4.)