A260304 a(n) = 5*a(n-1) - 5*a(n-2) for n>1, a(0)=2, a(1)=3.
2, 3, 5, 10, 25, 75, 250, 875, 3125, 11250, 40625, 146875, 531250, 1921875, 6953125, 25156250, 91015625, 329296875, 1191406250, 4310546875, 15595703125, 56425781250, 204150390625, 738623046875, 2672363281250, 9668701171875, 34981689453125, 126564941406250
Offset: 0
Links
- Index entries for linear recurrences with constant coefficients, signature (5,-5).
Crossrefs
Programs
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Magma
[n le 2 select n+1 else 5*Self(n-1)-5*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Nov 23 2015
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Mathematica
Table[((5 + 2 Sqrt[5]) ((5 - Sqrt[5])/2)^n + (5 - 2 Sqrt[5]) ((5 + Sqrt[5])/2)^n)/5, {n, 0, 30}] RecurrenceTable[{a[0] == 2, a[1] == 3, a[n] == 5 a[n - 1] - 5 a[n - 2]}, a, {n, 0, 30}] (* Bruno Berselli, Nov 23 2015 *) -
PARI
a(n)=([0,1; -5,5]^n*[2;3])[1,1] \\ Charles R Greathouse IV, Jul 26 2016
Formula
G.f.: (2 - 7*x)/(1 - 5*x + 5*x^2).
a(n) = ((5 + 2*sqrt(5))*((5 - sqrt(5))/2)^n + (5 - 2*sqrt(5))*((5 + sqrt(5))/2)^n)/5.
Extensions
Edited by Bruno Berselli, Nov 23 2015
Comments