A167122 a(n) = 20*a(n-1) - 64*a(n-2) + 3 for n > 2; a(0) = 1, a(1) = 22, a(2) = 378.

1, 22, 378, 6155, 98911, 1584303, 25355759, 405719791, 6491627247, 103866478319, 1661865422575, 26589853839087, 425437689736943, 6807003149037295, 108912050837581551, 1742592815213244143, 27881485050659663599

Offset: 0

Author

Klaus Brockhaus, Oct 27 2009

Keywords

• nonn

Comments

lim_{n -> infinity} a(n)/a(n-1) = 16.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (21, -84, 64).

Crossrefs

Cf. A166912, A166913, A167120, A167121.

Programs

Magma

[ n le 2 select 21*n-20 else n eq 3 select 378 else 20*Self(n-1)-64*Self(n-2)+3: n in [1..17] ];

Mathematica

CoefficientList[Series[(1 + x + x^3)/((1-x)*(1-4*x)*(1-16*x)), {x, 0, 10}], x] (* G. C. Greubel, Jun 04 2016 *)
LinearRecurrence[{21,-84,64},{1,22,378,6155},20] (* Harvey P. Dale, Sep 26 2023 *)

Formula

a(n) = (1451*16^n - 540*4^n + 64)/960, for n > 0.

G.f.: (1 + x + x^3)/((1-x)*(1-4*x)*(1-16*x)).

E.g.f.: (1/960)*(-15 + 64*exp(x) - 540*exp(4*x) + 1451*exp(16*x)). - G. C. Greubel, Jun 04 2016