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A163470
a(n) = 8*a(n-1) - 13*a(n-2) for n > 1; a(0) = 3, a(1) = 15.
2
3, 15, 81, 453, 2571, 14679, 84009, 481245, 2757843, 15806559, 90600513, 519318837, 2976744027, 17062807335, 97804786329, 560621795277, 3213512139939, 18420013780911, 105584452428081, 605215440272805
OFFSET
0,1
COMMENTS
Binomial transform of A083881 without initial 1. Inverse binomial transform of A163471.
FORMULA
a(n) = ((3+sqrt(3))*(4+sqrt(3))^n + (3-sqrt(3))*(4-sqrt(3))^n)/2.
G.f.: (3-9*x)/(1-8*x+13*x^2).
a(n) = 3*A162557(n). - R. J. Mathar, Jun 14 2016
E.g.f.: (1/2)*exp(4*x)*(6*cosh(sqrt(3)*x) + 2*sqrt(3)*sinh(sqrt(3)*x)). - G. C. Greubel, Jul 25 2017
MATHEMATICA
LinearRecurrence[{8, -13}, {3, 15}, 50] (* G. C. Greubel, Jul 25 2017 *)
PROG
(Magma) [ n le 2 select 12*n-9 else 8*Self(n-1)-13*Self(n-2): n in [1..22] ];
(PARI) x='x+O('x^50); Vec((3-9*x)/(1-8*x+13*x^2)) \\ G. C. Greubel, Jul 25 2017
CROSSREFS
Sequence in context: A233020 A246020 A084120 * A122868 A264225 A343975
KEYWORD
nonn,easy
AUTHOR
Klaus Brockhaus, Aug 11 2009
STATUS
approved