A201864 a(n) = ((F(n-1)+F(n-2))-1)/2 if F(n) is odd, otherwise a(n) = ((F(n-1)+F(n-2))-2)/2, where F(n) = A000045(n) is the n-th Fibonacci number.

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

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

a(n) = F(n) - ceiling(F(n-1)/2) - ceiling(F(n-2)/2). - Chunqing Liu, Aug 21 2023

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, A131534.

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