A170933 a(n) = A000930(n) + A000930(n+3) + 4.

7, 8, 9, 12, 16, 21, 29, 41, 58, 83, 120, 174, 253, 369, 539, 788, 1153, 1688, 2472, 3621, 5305, 7773, 11390, 16691, 24460, 35846, 52533, 76989, 112831, 165360, 242345, 355172, 520528, 762869, 1118037

Offset: 0

Author

N. J. A. Sloane, Feb 10 2010

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Z. Skupien, Sparse Hamiltonian 2-decompositions together with exact count of numerous Hamiltonian cycles, Discr. Math., 309 (2009), 6382-6390.
• Index entries for linear recurrences with constant coefficients, signature (2,-1,1,-1).

Programs

Mathematica

CoefficientList[Series[(7 - 6*x - 5*x^3)/(1 - 2*x + x^2 - x^3 + x^4), {x, 0, 50}], x] (* G. C. Greubel, Apr 26 2017 *)
LinearRecurrence[{2,-1,1,-1},{7,8,9,12},40] (* Harvey P. Dale, Aug 07 2021 *)

PARI

x='x+O('x^50); Vec((7 - 6*x - 5*x^3)/(1 - 2*x + x^2 - x^3 + x^4)) \\ G. C. Greubel, Apr 26 2017

Formula

G.f.: (7-6*x-5*x^3)/(1-2*x+x^2-x^3+x^4). - Colin Barker, Dec 30 2011

a(n) = a(n-1) + a(n-3) - 4 for n>2. - Greg Dresden, Feb 09 2020