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%I #3 Mar 30 2012 17:39:33
%S 1,1,1,2,6,19,61,197,637,2060,6662,21545,69677,225337,728745,2356778,
%T 7621874,24649315,79716449,257804821,833746693,2696355892,8720076682,
%U 28200927617,91202445513,294950796673,953877628705,3084862088210,9976514614558,32264276654339,104343409321397,337448974463477,1091317708583837,3529346452933372,11413987225587534
%N a(n) = 4*a(n-1) - 3*a(n-2) + 2*a(n-3) - 1*a(n-4).
%C a(n)/a(n-1) tends to 3.2340228928..., an eigenvalue of the matrix X and a root to x^4 - 4*x^3 + 3*x^2 - 2*x + 1 = 0.
%F a(n) = 4*a(n-1) - 3*a(n-2) + 2*a(n-3) - 1*a(n-4); a>4. Let X = the 4 X 4 matrix [0,1,0,0; 0,0,1,0; 0,0,0,1; -1,2,-3,4]. X^n * [1,1,1,1] = [a(n), a(n+1), a(n+2), a(n+3)].
%F O.g.f.: -x(-1+3x+x^3)/(1-4x+3x^2-2x^3+x^4). - _R. J. Mathar_, Apr 03 2008
%e a(7) = 61 = 4*a(6) - 3*a(5) + 2*a(4) - 1*a(3) = 4*19 - 3*6 + 2*2 - 1*1.
%e X^4 * [1,1,1,1] = [a(4), a(5), a(6), a(7)] = [2, 6, 19, 61].
%K nonn
%O 1,4
%A _Gary W. Adamson_, Mar 28 2008
%E More terms from _R. J. Mathar_, Apr 03 2008