A190973 a(n) = 7*a(n-1) - 4*a(n-2), with a(0) = 0, a(1) = 1.

0, 1, 7, 45, 287, 1829, 11655, 74269, 473263, 3015765, 19217303, 122458061, 780337215, 4972528261, 31686348967, 201914329725, 1286654912207, 8198927066549, 52245869817015, 332925380452909, 2121494183902303, 13518757765504485, 86145327622922183

Offset: 0

Author

Vladimir Joseph Stephan Orlovsky, May 24 2011

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (7,-4).

Crossrefs

Cf. A190958 (index to generalized Fibonacci sequences).

Programs

GAP

a:=[0,1];; for n in [3..30] do a[n]:=7*a[n-1]-4*a[n-2]; od; a; # G. C. Greubel, Dec 24 2019

Magma

I:=[0,1]; [n le 2 select I[n] else 7*Self(n-1) - 4*Self(n-2): n in [1..20]]; // G. C. Greubel, Dec 24 2019

Maple

seq( simplify(2^(n-1)*ChebyshevU(n-1, 7/4)), n=0..30); # G. C. Greubel, Dec 24 2019

Mathematica

LinearRecurrence[{7, -4}, {0, 1}, 30]
Table[2^(n - 1) * ChebyshevU[n - 1, 7/4], {n, 0, 30}] (* G. C. Greubel, Dec 24 2019 *)

PARI

vector(31, n, 2^(n-2)*polchebyshev(n-2, 2, 7/4) ) \\ G. C. Greubel, Dec 24 2019

Sage

[2^(n-1)*chebyshev_U(n-1,7/4) for n in (0..30)] # G. C. Greubel, Dec 24 2019

Formula

a(n) = ((7/2 + 1/2*sqrt(33))^n - (7/2 - 1/2*sqrt(33))^n)/sqrt(33). - Giorgio Balzarotti, May 28 2011

G.f.: x/(1 - 7*x + 4*x^2). - Philippe Deléham, Oct 12 2011