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a(n) = -4*a(n-3) + 11*a(n-2) - a(n-1), a(0) = 13, a(1) = -19, a(2) = 162
3

%I #7 Jul 28 2015 16:13:17

%S 13,-19,162,-423,2281,-7582,34365,-126891,535234,-2068495,8463633,

%T -33358014,134731957,-535524643,2151008226,-8580707127,34383896185,

%U -137375707486,549921394029,-2198589761115,8797227925378

%N a(n) = -4*a(n-3) + 11*a(n-2) - a(n-1), a(0) = 13, a(1) = -19, a(2) = 162

%C a(n) + A153267(n) = 4*A001519(n) (apart from initial terms). The generating floretion Z = X*Y with X = 1.5'i + 0.5i' + .25(ii + jj + kk + ee) and Y = 0.5'i + 1.5i' + .25(ii + jj + kk + ee)

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (-1, 11, -4).

%F a(n) = 2*(-4)^n + (-2/5*sqrt(5)-1)*(3/2+1/2*sqrt(5))^n + (2/5*sqrt(5)-1)*(3/2-1/2*sqrt(5))^n

%F a(n)=A001519(n+3)+8*(-4)^n. G.f.: (13-6x)/((1+4x)(1-3x+x^2)). [From _R. J. Mathar_, Jan 05 2009]

%e a(4) = -1*(-423) + 11*162 - 4*(-19) = 2281

%Y A153267, A153265, A001519

%K easy,sign

%O 0,1

%A _Creighton Dement_, Jan 02 2009