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A163471 a(n) = 10*a(n-1) - 22*a(n-2) for n > 1; a(0) = 3, a(1) = 18. 3
3, 18, 114, 744, 4932, 32952, 221016, 1485216, 9989808, 67223328, 452457504, 3045661824, 20502553152, 138020971392, 929153544576, 6255074075136, 42109362770688, 283481998053888, 1908413999583744, 12847536038651904 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
Binomial transform of A163470. Inverse binomial transform of A163472.
LINKS
FORMULA
a(n) = ((3+sqrt(3))*(5+sqrt(3))^n + (3-sqrt(3))*(5-sqrt(3))^n)/2.
G.f.: (3-12*x)/(1-10*x+22*x^2).
E.g.f.: exp(5*x)*( 3*cosh(sqrt(3)*x) + sqrt(3)*sinh(sqrt(3)*x) ). - G. C. Greubel, Jul 26 2017
MATHEMATICA
LinearRecurrence[{10, -22}, {3, 18}, 50] (* G. C. Greubel, Jul 26 2017 *)
PROG
(Magma) [ n le 2 select 15*n-12 else 10*Self(n-1)-22*Self(n-2): n in [1..20] ];
(PARI) x='x+O('x^50); Vec((3-12*x)/(1-10*x+22*x^2)) \\ G. C. Greubel, Jul 26 2017
CROSSREFS
Sequence in context: A346578 A213099 A199259 * A054122 A213230 A201695
KEYWORD
nonn
AUTHOR
Klaus Brockhaus, Aug 11 2009
STATUS
approved

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Last modified March 29 08:48 EDT 2024. Contains 371268 sequences. (Running on oeis4.)