A190961 a(n) = 3*a(n-1) - 7*a(n-2), with a(0)=0, a(1)=1.

0, 1, 3, 2, -15, -59, -72, 197, 1095, 1906, -1947, -19183, -43920, 2521, 315003, 927362, 577065, -4760339, -18320472, -21639043, 63326175, 341451826, 581072253, -646946023, -6008343840, -13496409359, 1569178803, 99182401922, 286562954145, 165412048981

Offset: 0

Author

Vladimir Joseph Stephan Orlovsky, May 24 2011

Keywords

• sign
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-7).

Crossrefs

Cf. A190958 (index to generalized Fibonacci sequences).

Programs

Magma

I:=[0,1]; [n le 2 select I[n] else 3*Self(n-1) - 7*Self(n-2): n in [1..30]]; // G. C. Greubel, Jan 25 2018

Mathematica

LinearRecurrence[{3,-7}, {0,1}, 50]

PARI

x='x+O('x^30); concat([0], Vec(x/(1-3*x+7*x^2))) \\ G. C. Greubel, Jan 25 2018

Formula

G.f.: x/(1-3*x+7*x^2). - Philippe Deléham, Oct 11 2011

E.g.f.: 2*exp(3*x/2)*sin(sqrt(19)*x/2)/sqrt(19). - Stefano Spezia, Jul 28 2025