A170934 a(n) = b(n) + b(n+1) + 2, where b() = A000930().

4, 4, 5, 7, 9, 12, 17, 24, 34, 49, 71, 103, 150, 219, 320, 468, 685, 1003, 1469, 2152, 3153, 4620, 6770, 9921, 14539, 21307, 31226, 45763, 67068, 98292, 144053, 211119, 309409, 453460, 664577, 973984, 1427442, 2092017, 3065999, 4493439, 6585454, 9651451

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[-(3*x^3 - x^2 + 4*x - 4)/((x - 1)*(x^3 + x - 1)), {x, 0, 50}], x] (* G. C. Greubel, Apr 26 2017 *)
LinearRecurrence[{2,-1,1,-1},{4,4,5,7},50] (* Harvey P. Dale, Jul 10 2020 *)

PARI

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

Formula

From Colin Barker, Jul 25 2013: (Start)

a(n) = 2*a(n-1)-a(n-2)+a(n-3)-a(n-4).

G.f.: -(3*x^3-x^2+4*x-4) / ((x-1)*(x^3+x-1)). (End)

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

Extensions

More terms from Colin Barker, Jul 25 2013