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A201864 ((F(n-1)+F(n-2))-1)/2 if F(n) is odd, otherwise ((F(n-1)+F(n-2))-2)/2, where F(n)=A000045(n) is the n-th Fibonacci number. 1
0, 0, 0, 1, 2, 3, 6, 10, 16, 27, 44, 71, 116, 188, 304, 493, 798, 1291, 2090, 3382, 5472, 8855, 14328, 23183, 37512, 60696, 98208, 158905, 257114, 416019, 673134, 1089154, 1762288, 2851443, 4613732, 7465175, 12078908, 19544084, 31622992, 51167077, 82790070 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

See also similar sequence A130578.

a(n) is the number of segments connected contained in a graph with, F(n-1) is the number of vertex, and F(n-2) is the numbers of sides.

LINKS

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

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

FORMULA

G.f.: x^4*(1+x)/((1-x)(1+x+x^2)(1-x-x^2)). - Alois P. Heinz, Dec 13 2011

a(n) = (1/2)*(A000045(n)-A131534(n+1)). - Bruno Berselli, Dec 14 2011

MAPLE

a:= n-> (Matrix(5, (i, j)-> `if`(i=j-1, 1, `if`(i=5,

        [-1, -1, 1, 1, 1][j], 0)))^n. <<-1, 0, 0, 0, 1>>)[1, 1]:

seq(a(n), n=1..50);  # Alois P. Heinz, Dec 13 2011

MATHEMATICA

CoefficientList[Series[x^3*(1+x)/((1-x)(1+x+x^2)(1-x-x^2)), {x, 0, 30}], x] (* Vincenzo Librandi, Mar 20 2012 *)

PROG

(MAGMA) [IsOdd(Fibonacci(n)) select (Fibonacci(n)-1)/2 else Fibonacci(n)/2-1: n in [1..41]];  // Bruno Berselli, Dec 14 2011

CROSSREFS

Cf. A000045.

Sequence in context: A023561 A243735 A034419 * A198200 A294444 A066895

Adjacent sequences:  A201861 A201862 A201863 * A201865 A201866 A201867

KEYWORD

nonn,easy

AUTHOR

Giovanni Teofilatto, Dec 06 2011

STATUS

approved

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Last modified September 25 08:41 EDT 2020. Contains 337335 sequences. (Running on oeis4.)