A190441 a(n) = 4*a(n-1) + 39*a(n-2), with a(0)=0, a(1)=1.
0, 1, 4, 55, 376, 3649, 29260, 259351, 2178544, 18828865, 160278676, 1375440439, 11752630120, 100652697601, 860963365084, 7369308666775, 63054805905376, 539622261625729, 4617626476812580, 39515774110653751, 338150529038305624, 2893717306468718785
Offset: 0
Links
- Bruno Berselli, Table of n, a(n) for n = 0..300
- Index entries for linear recurrences with constant coefficients, signature (4,39).
Programs
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Magma
[n le 2 select n-1 else 4*Self(n-1)+39*Self(n-2): n in [1..22]];
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Mathematica
a = {0, 1}; Do[AppendTo[a, 4 a[[-1]] + 39 a[[-2]]], {20}]; a (* Bruno Berselli, Dec 26 2012 *) CoefficientList[Series[x / (1 - 4 x - 39 x^2), {x, 0, 25}], x] (* Vincenzo Librandi, Aug 19 2013 *) LinearRecurrence[{4,39},{0,1},30] (* Harvey P. Dale, Aug 21 2021 *) -
Maxima
a[0]:0$ a[1]:1$ a[n]:=4*a[n-1]+39*a[n-2]$ makelist(a[n], n, 0, 17);
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PARI
x='x+O('x^30); concat([0], Vec(x/(1-4*x-39*x^2))) \\ G. C. Greubel, Dec 30 2017
Formula
G.f.: x/(1-4*x-39*x^2).
a(n) = ((2+sqrt(43))^n - (2-sqrt(43))^n)/(2*sqrt(43)).