A137212 a(n) = 5*a(n-1) - 5*a(n-2) - 3*a(n-3).
0, 0, 1, 5, 20, 72, 245, 805, 2584, 8160, 25465, 78773, 242060, 740040, 2253581, 6841525, 20719600, 62629632, 189025585, 569820965, 1716088004, 5164258440, 15531389285, 46687390213, 140287229320, 421405027680, 1265526821161
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (5,-5,-3).
Programs
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Magma
[n le 3 select Floor((n-1)/2) else 5*Self(n-1) -5*Self(n-2) -3*Self(n-3): n in [1..31]]; // G. C. Greubel, Jan 05 2022
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Mathematica
LinearRecurrence[{5,-5,-3},{0,0,1},30] (* Harvey P. Dale, Nov 28 2013 *) -
Sage
[(2*3^n - lucas_number2(n+1, 2, -1))/4 for n in (0..30)] # G. C. Greubel, Jan 05 2022
Formula
a(n) = A193519(n)/2.
From R. J. Mathar, Mar 17 2008: (Start)
O.g.f.: x^2/((1-3*x)*(1-2*x-x^2)).
a(n) = (3^n - A078057(n))/2 . (End)
a(n) = (1/4)*(2*3^n - A002203(n+1)). - G. C. Greubel, Jan 05 2022