A185265 a(0)=1, a(1)=2; thereafter a(n) = f(n-1) + f(n-2) where f() = A164387().

1, 2, 3, 6, 12, 22, 39, 70, 127, 231, 419, 759, 1375, 2492, 4517, 8187, 14838, 26892, 48739, 88335, 160099, 290164, 525894, 953132, 1727460, 3130855, 5674373, 10284254, 18639219, 33781788, 61226235, 110966650, 201116358, 364504015, 660628396, 1197325296, 2170036700, 3932982369, 7128151480

Offset: 0

Author

N. J. A. Sloane, Mar 31 2011

Keywords

• nonn
• easy

Comments

Arises in studying lunar arithmetic.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• D. Applegate, M. LeBrun and N. J. A. Sloane, Dismal Arithmetic [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic" - the old name was too depressing]
• Index entries for linear recurrences with constant coefficients, signature (1,1,0,1,1).

Crossrefs

Cf. A164387, A079976.

Programs

Mathematica

CoefficientList[Series[-(x + 1)*(x^4 + x^3 + 1)/(x^5 + x^4 + x^2 + x - 1), {x, 0, 50}], x] (* G. C. Greubel, Jun 25 2017 *)

PARI

x='x+O('x^50); Vec(-(x+1)*(x^4+x^3+1)/(x^5+x^4+x^2+x-1)) \\ G. C. Greubel, Jun 25 2017

Formula

Satisfies the same recurrence as A164387 and A079976, although with different initial conditions.

From Colin Barker, Jul 25 2013: (Start)

a(n) = a(n-1) + a(n-2) + a(n-4) + a(n-5) for n>5.

G.f.: -(x+1)*(x^4+x^3+1) / (x^5+x^4+x^2+x-1). (End)