A105579 - OEIS

%I #20 Mar 08 2024 12:14:52

%S 1,3,4,1,-4,-3,8,17,4,-27,-32,25,92,45,-136,-223,52,501,400,-599,

%T -1396,-195,2600,2993,-2204,-8187,-3776,12601,20156,-5043,-45352,

%U -35263,55444,125973,15088,-236855,-267028,206685,740744,327377,-1154108,-1808859,499360,4117081,3118364,-5115795,-11352520

%N a(n+3) = 2a(n+2) - 3a(n+1) + 2a(n); a(0) = 1, a(1) = 3, a(2) = 4.

%C Floretion Algebra Multiplication Program, FAMP Code: famseq[.5'j + .5'k + .5j' + .5k' + .5'ii' + .5e]

%F a(n+1) - a(n) = A002249(n).

%F a(n) = 2*a(n-1)-3*a(n-2)+2*a(n-3). G.f.: (1+x+x^2)/((1-x)*(1-x+2*x^2)). [_Colin Barker_, Mar 27 2012]

%t Table[(3 - ((1-I*Sqrt[7])^n + (1+I*Sqrt[7])^n)/2^n)/2 // Simplify, {n, 1, 50}] (* _Jean-François Alcover_, Jun 04 2017 *)

%Y Cf. A002249, A014551, A078020, A105577, A105578, A105580.

%Y Cf. Equals (1/2) [A107920(n+4) - 2*A107920(n-1) + 3 ].

%K sign,easy

%O 0,2

%A _Creighton Dement_, Apr 14 2005

%E Corrected by _T. D. Noe_, Nov 07 2006