A164552 a(n) = 12*a(n-1)-30*a(n-2) for n > 1; a(0) = 1, a(1) = 10.

1, 10, 90, 780, 6660, 56520, 478440, 4045680, 34194960, 288969120, 2441780640, 20632294080, 174334109760, 1473040494720, 12446462643840, 105166336884480, 888602163298560, 7508235853048320, 63440765337623040, 536042108460026880

Offset

0,2

Comments

Binomial transform of A164551. Inverse binomial transform of A164553.

Links

Table of n, a(n) for n=0..19.

Index entries for linear recurrences with constant coefficients, signature (12, -30).

Formula

a(n) = ((3+2*sqrt(6))*(6+sqrt(6))^n+(3-2*sqrt(6))*(6-sqrt(6))^n)/6.

G.f.: (1-2*x)/(1-12*x+30*x^2).

Mathematica

LinearRecurrence[{12, -30}, {1, 10}, 20] (* Harvey P. Dale, Apr 19 2019 *)

Prog

(Magma) [ n le 2 select 9*n-8 else 12*Self(n-1)-30*Self(n-2): n in [1..20] ];
(PARI) a(n)=([0, 1; -30, 12]^n*[1; 10])[1, 1] \\ Charles R Greathouse IV, May 28 2026

Crossrefs

Cf. A164551, A164553.

Sequence in context: A199940 A004985 A276020 * A057086 A092420 A010579

Adjacent sequences: A164549 A164550 A164551 * A164553 A164554 A164555

Keyword

nonn,easy,changed

Author

Klaus Brockhaus, Aug 15 2009

Status

approved