A142879 a(n) = 5*a(n-3) - a(n-6) with terms 1..6 as 0, 1, 2, 5, 7, 9.

0, 1, 2, 5, 7, 9, 25, 34, 43, 120, 163, 206, 575, 781, 987, 2755, 3742, 4729, 13200, 17929, 22658, 63245, 85903, 108561, 303025, 411586, 520147, 1451880, 1972027, 2492174, 6956375, 9448549, 11940723, 33329995, 45270718, 57211441, 159693600

Offset

1,3

Links

Colin Barker, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (0,0,5,0,0,-1).

Formula

a(n) = 2*a(n - 1) + a(n - 2) if 3 | n, a(n) = a(n - 1) + a(n - 2) if n = 1 mod 3, and a(n) = 2*a(n - 1) - a(n - 2) if n = 2 mod 3.

G.f.: x^2*(1+2*x+5*x^2+2*x^3-x^4) / (1-5*x^3+x^6). - Colin Barker, Jan 08 2013

Mathematica

Clear[a, n]; a[0] = 0; a[1] = 1; a[n_] := a[n] = If[Mod[n, 3] == 0, 2*a[n - 1] + a[n - 2], If[Mod[n, 3] == 1, a[n - 1] + a[n - 2], 2*a[n - 1] - a[n - 2]]]; b = Table[a[n], {n, 0, 50}]
LinearRecurrence[{0, 0, 5, 0, 0, -1}, {0, 1, 2, 5, 7, 9}, 40] (* Harvey P. Dale, Apr 06 2016 *)

Prog

(PARI) a=vector(20); a[1]=1; a[2]=2; for(n=3, #a, if(n%3==0, a[n]=2*a[n-1]+a[n-2], if(n%3==1, a[n]=a[n-1]+a[n-2], a[n]=2*a[n-1]-a[n-2]))); concat(0, a) \\ Colin Barker, Jan 30 2016
(PARI) concat(0, Vec(x^2*(1+2*x+5*x^2+2*x^3-x^4)/(1-5*x^3+x^6) + O(x^50))) \\ Colin Barker, Jan 30 2016

Crossrefs

Cf. A119016, A002965, A002530, A048788.

Sequence in context: A286356 A086422 A046880 * A284167 A108118 A099477

Adjacent sequences: A142876 A142877 A142878 * A142880 A142881 A142882

Keyword

nonn,easy

Author

Roger L. Bagula and Gary W. Adamson, Sep 28 2008

Extensions

New name from Colin Barker and Charles R Greathouse IV, Jan 08 2013

Status

approved