%I #21 Mar 12 2024 12:16:17

%S 1,6,20,57,154,408,1073,2814,7372,19305,50546,132336,346465,907062,

%T 2374724,6217113,16276618,42612744,111561617,292072110,764654716,

%U 2001892041,5241021410,13721172192,35922495169,94046313318,246216444788

%N a(n) = 4*a(n-1) - 4*a(n-2) + a(n-3), n >= 3; a(0)=1, a(1)=6, a(2)=20.

%C Floretion Algebra Multiplication Program, FAMP Code: 4tessumseq[ + .25'i + .25i' + .25'ii' + .25'jj' + .25'kk' + .25'jk' + .25'kj' + .25e], sumtype: (Y[15], *, vesy)

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

%F a(n) - a(n-1) = A054486(n+1).

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

%F a(n) = A027941(n+1) +2*A027941(n). - _R. J. Mathar_, Sep 11 2019

%t Join[{a=1,b=6},Table[c=3*b-1*a+3;a=b;b=c,{n,60}]] (* _Vladimir Joseph Stephan Orlovsky_, Jan 28 2011 *)

%t LinearRecurrence[{4,-4,1},{1,6,20},30] (* _Harvey P. Dale_, Apr 14 2016 *)

%Y Cf. A054486.

%K easy,nonn

%O 0,2

%A _Creighton Dement_, Aug 18 2005