OFFSET
0,1
COMMENTS
Also distinct compositions of the wheel graph W_n. - Ralf Stephan, Jan 02 2003
LINKS
A. Knopfmacher and M. E. Mays, Graph Compositions. I: Basic Enumeration, Integers 1(2001), #A04.
Index entries for linear recurrences with constant coefficients, signature (5,-8,5,-1).
FORMULA
a(n) = 3*a(n-1) - a(n-2) + n - 1.
G.f.: (2 - 8*x + 11*x^2 - 4*x^3)/((1-3*x+x^2)*(1-x)^2).
a(n) = Lucas(2*n) - n. - G. C. Greubel, Oct 12 2019
MAPLE
with(combinat); seq(fibonacci(2*n+1)+fibonacci(2*n-1)-n, n=0..50); # G. C. Greubel, Oct 12 2019
MATHEMATICA
Table[LucasL[2*n]-n, {n, 0, 50}] (* G. C. Greubel, Oct 12 2019 *)
PROG
(PARI) a(n)=fibonacci(2*n+1)+fibonacci(2*n-1)-n
(Magma) [Lucas(2*n) - n: n in [0..50]]; // G. C. Greubel, Oct 12 2019
(Sage) [lucas_number2(2*n, 1, -1) - n for n in range(50)] # G. C. Greubel, Oct 12 2019
(GAP) List([0..50], n-> Lucas(1, -1, 2*n)[2] - n ); # G. C. Greubel, Oct 12 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved