A108140 - OEIS

%I #9 Apr 07 2023 14:06:28

%S 1,1,1,1,0,4,17,55,161,449,1220,3266,8667,22879,60203,158107,414728,

%T 1087064,2848061,7459703,19535229,51152749,133933964,350666854,

%U 918095255,2403665279,6292975607,16475382935,43133369616,112925043724

%N a(n) = 4*a(n-1) -3*a(n-2) -2*a(n-3) +a(n-4), n>8.

%H Roger Bagula, <a href="http://victorian.fortunecity.com/carmelita/435/">Factoring Double Fibonacci Sequences</a>, 2000.

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-3,-2,1).

%F a(n) = -A000045(n+2)/2 + A001906(n-1)/2, n>3. [Sep 28 2009]

%F G.f.: (-1+2*x^7-2*x^6-8*x^5-2*x^3+3*x)/((x^2+x-1)*(x^2-3*x+1)). [Maksym Voznyy (voznyy(AT)mail.ru), Jul 27 2009]

%t F[1] = 1; F[2] = 1; F[3] = 1; F[4] = 1; F[n__] := F[n] = 4*F[n - 1] - 3*F[n - 2] - 2*F[n - 3] + F[n - 4] a = Table[Abs[F[n]], {n, 1, 50}]

%Y Cf. A000045, A056015, A056016.

%K nonn,easy

%O 0,6

%A _Roger L. Bagula_, Jun 05 2005

%E Definition replaced by recurrence by the Associate Editors of the OEIS, Sep 28 2009