A109164 a(n) = 4*a(n-1) - 4*a(n-2) + a(n-3), n >= 3; a(0)=1, a(1)=6, a(2)=20.

1, 6, 20, 57, 154, 408, 1073, 2814, 7372, 19305, 50546, 132336, 346465, 907062, 2374724, 6217113, 16276618, 42612744, 111561617, 292072110, 764654716, 2001892041, 5241021410, 13721172192, 35922495169, 94046313318, 246216444788

Offset: 0

Author

Creighton Dement, Aug 18 2005

Keywords

• easy
• nonn

Comments

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)

Links

• Index entries for linear recurrences with constant coefficients, signature (4,-4,1).

Crossrefs

Cf. A054486.

Programs

Mathematica

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 *)
LinearRecurrence[{4,-4,1},{1,6,20},30] (* Harvey P. Dale, Apr 14 2016 *)

Formula

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

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

a(n) = A027941(n+1) +2*A027941(n). - R. J. Mathar, Sep 11 2019