A056016 - OEIS

%I #19 Oct 27 2023 22:00:46

%S 1,1,1,-4,6,-9,16,-29,51,-89,156,-274,481,-844,1481,-2599,4561,-8004,

%T 14046,-24649,43256,-75909,133211,-233769,410236,-719914,1263361,

%U -2217044,3890641,-6827599,11981601,-21026244,36898486,-64752329,113632416,-199410989,349941891,-614105209

%N a(n) = -2*a(n - 1) -a(n - 2) -a(n - 3), a(0) = a(1) = a(2) = 1.

%H Roger L. Bagula, <a href="https://web.archive.org/web/20010901155049/http://www.crosswinds.net/~translight/fib_double.html">Factoring Double Fibonacci Sequences, 2000</a> [Wayback Machine link from _Felix Fröhlich_, Nov 21 2019]

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (-2,-1,-1).

%F O.g.f.: (1+3x+4x^2)/(1+2x+x^2+x^3). - _R. J. Mathar_, Aug 22 2008

%t LinearRecurrence[{-2,-1,-1},{1,1,1},40] (* _Harvey P. Dale_, Jun 09 2016 *)

%o (Magma) [n le 3 select 1 else -2*Self(n-1)-Self(n-2)-Self(n-3):n in [1..37]]; // _Marius A. Burtea_, Nov 21 2019

%K sign

%O 0,4

%A _Asher Auel_, Jun 06 2000

%E Inserted a(0) and a(1) by _R. J. Mathar_, Aug 23 2008