A162757 a(n) = 12*a(n-1)-33*a(n-2) for n > 1; a(0) = 1, a(1) = 7.

1, 7, 51, 381, 2889, 22095, 169803, 1308501, 10098513, 78001623, 602768547, 4659169005, 36018666009, 278471414943, 2153041001019, 16646935319109, 128712870795681, 995205584017575, 7694942271953427, 59497522990861149

Offset: 0

Author

Klaus Brockhaus, Jul 13 2009

Keywords

• nonn

Comments

Sixth binomial transform of A108411. Binomial transform of A162558. Inverse binomial transform of A162758.

Links

• Index entries for linear recurrences with constant coefficients, signature (12, -33).

Crossrefs

Cf. A108411 (powers of 3 repeated), A162558, A162758.

Programs

Magma

[ n le 2 select 6*n-5 else 12*Self(n-1)-33*Self(n-2): n in [1..20] ];

Formula

a(n) = ((3+sqrt(3))*(6+sqrt(3))^n+(3-sqrt(3))*(6-sqrt(3))^n)/6.

G.f.: (1-5*x)/(1-12*x+33*x^2).