A167120 a(n) = 20*a(n-1) - 64*a(n-2) + 1 for n > 2; a(0) = 1, a(1) = 22, a(2) = 376.
1, 22, 376, 6113, 98197, 1572709, 25169573, 402738085, 6443909029, 103102943141, 1649648684965, 26394385338277, 422310190927781, 6756963156905893, 108111410918739877, 1729782576332820389, 27676521227857055653
Offset: 0
Keywords
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..200
- Index entries for linear recurrences with constant coefficients, signature (21,-84,64).
Programs
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Magma
[ n le 2 select 21*n-20 else n eq 3 select 376 else 20*Self(n-1)-64*Self(n-2)+1: n in [1..17] ];
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Mathematica
CoefficientList[Series[(1 + x - 2*x^2 + x^3)/((1 - x)*(1 - 4*x)*(1 - 16*x)), {x, 0, 10}], x] (* G. C. Greubel, Jun 04 2016 *) LinearRecurrence[{21,-84,64},{1,22,376,6113},20] (* Harvey P. Dale, Jul 13 2018 *)
Formula
a(n) = (4321*16^n - 1460*4^n + 64)/2880, for n > 0.
G.f.: (1 + x - 2*x^2 + x^3)/((1-x)*(1-4*x)*(1-16*x)).
E.g.f.: (1/2880)*(-45 + 64*exp(x) - 1460*exp(4*x) + 4321*exp(16*x)). - G. C. Greubel, Jun 04 2016
a(n) = 21*a(n-1) - 84*a(n-2) + 64*a(n-3). - Wesley Ivan Hurt, Aug 04 2025
Comments