A033550 a(n) = A005248(n) - n.

2, 2, 5, 15, 43, 118, 316, 836, 2199, 5769, 15117, 39592, 103670, 271430, 710633, 1860483, 4870831, 12752026, 33385264, 87403784, 228826107, 599074557, 1568397585, 4106118220, 10749957098, 28143753098, 73681302221, 192900153591

Offset

0,1

Comments

Also distinct compositions of the wheel graph W_n. - Ralf Stephan, Jan 02 2003

Links

Table of n, a(n) for n=0..27.

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

Cf. A000032, A000045.

Sequence in context: A208466 A098888 A089848 * A032130 A259101 A184313

Adjacent sequences: A033547 A033548 A033549 * A033551 A033552 A033553

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved