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

0,2

Comments

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

Links

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

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

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).

Mathematica

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

Prog

(Magma) [ n le 2 select 10*n-9 else 12*Self(n-1)-31*Self(n-2): n in [1..20] ];
(PARI) a(n)=([0, 1; -31, 12]^n*[1; 11])[1, 1] \\ Charles R Greathouse IV, May 30 2026

Crossrefs

Cf. A093145, A163147.

Sequence in context: A113403 A045624 A125399 * A037550 A138894 A287832

Adjacent sequences: A163143 A163144 A163145 * A163147 A163148 A163149

Keyword

nonn,easy,changed

Author

Klaus Brockhaus, Jul 21 2009

Status

approved