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A137212
a(n) = 5*a(n-1) - 5*a(n-2) - 3*a(n-3).
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
0,4
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
MATHEMATICA
LinearRecurrence[{5, -5, -3}, {0, 0, 1}, 30] (* Harvey P. Dale, Nov 28 2013 *)
PROG
(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
(Sage) [(2*3^n - lucas_number2(n+1, 2, -1))/4 for n in (0..30)] # G. C. Greubel, Jan 05 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul Curtz, Mar 06 2008
STATUS
approved