A163146 a(n) = 12*a(n-1)-31*a(n-2) for n > 1; a(0) = 1, a(1) = 11.

1, 11, 101, 871, 7321, 60851, 503261, 4152751, 34231921, 282047771, 2323383701, 19137123511, 157620587401, 1298196219971, 10692116430221, 88061314343551, 725280162785761, 5973461208779051, 49197849458990021, 405196896035729671

Offset: 0

Author

Klaus Brockhaus, Jul 21 2009

Keywords

• nonn

Comments

Binomial transform of A093145 without initial 0. Inverse binomial transform of A163147.

Links

• Index entries for linear recurrences with constant coefficients, signature (12,-31).

Crossrefs

Cf. A093145, A163147.

Programs

Magma

[ n le 2 select 10*n-9 else 12*Self(n-1)-31*Self(n-2): n in [1..20] ];

Mathematica

LinearRecurrence[{12,-31},{1,11},20] (* Harvey P. Dale, Apr 15 2019 *)

Formula

a(n) = ((1+sqrt(5))*(6+sqrt(5))^n+(1-sqrt(5))*(6-sqrt(5))^n)/2.

G.f.: (1-x)/(1-12*x+31*x^2).