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A187890 a(0)=0, a(1)=4, a(n)=a(n-1)+a(n-2)-1. 4
0, 4, 3, 6, 8, 13, 20, 32, 51, 82, 132, 213, 344, 556, 899, 1454, 2352, 3805, 6156, 9960, 16115, 26074, 42188, 68261, 110448, 178708, 289155, 467862, 757016, 1224877, 1981892, 3206768, 5188659, 8395426, 13584084, 21979509, 35563592, 57543100 (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).

FORMULA

G.f. ( -x^2*(-4+5*x) ) / ( (x-1)*(x^2+x-1) ). - R. J. Mathar, Mar 15 2011

a(n)= 1+A001060(n-2), n>2. - R. J. Mathar, Mar 15 2011

a(n)=1-1/2*((1/2+1/2*sqrt(5))^(n-1)+(1/2-1/2*sqrt(5))^(n-1))+7/10*sqrt(5)*((1/2+1/2*sqrt(5))^(n-1)-(1/2-1/2 *sqrt(5))^(n-1)). - Paolo P. Lava, Jun 06 2011

MATHEMATICA

Join[{a = 0, b = 4}, Table[c = a+b-1; a=b; b=c, {n, 100}]]

LinearRecurrence[{2, 0, -1}, {0, 4, 3}, 40] (* Harvey P. Dale, Sep 25 2013 *)

CoefficientList[Series[(-x (-4 + 5 x))/((x - 1) (x^2 + x - 1)), {x, 0, 40}], x] (* Vincenzo Librandi, Sep 26 2013 *)

CROSSREFS

Cf. A000071, A001611, A001612.

Sequence in context: A211362 A211246 A197829 * A305581 A016702 A198610

Adjacent sequences:  A187887 A187888 A187889 * A187891 A187892 A187893

KEYWORD

nonn,easy

AUTHOR

Vladimir Joseph Stephan Orlovsky, Mar 15 2011

STATUS

approved

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Last modified November 18 01:20 EST 2018. Contains 317279 sequences. (Running on oeis4.)