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Column 0 of triangle A091700.
2

%I #13 May 04 2023 06:06:19

%S 1,2,7,23,78,264,895,3034,10286,34872,118225,400813,1358859,4606881,

%T 15618510,52950761,179516682,608607667,2063336333,6995240208,

%U 23715661274,80402183905,272584057514,924129977596,3133038018732,10621803712455,36010643162123

%N Column 0 of triangle A091700.

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

%F G.f.: (1-x-x^2)/(1-3x-2x^2+2x^3+x^4).

%F From _Philippe Deléham_, May 04 2023: (Start)

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

%F a(n) = M^n [1, 1] where M = [2, 1, 1, 1 ; 1, 1, 1, 0 ; 1, 1, 0, 0 ; 1, 0, 0, 0 ] . (End)

%Y Cf. A091700.

%K nonn,easy

%O 0,2

%A _Christian G. Bower_, Jan 29 2004