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
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).
Programs
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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 *) -
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
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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
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
Extensions
New name from Colin Barker and Charles R Greathouse IV, Jan 08 2013