A011920 a(n) = b(n)*(b(n)+1) = b(n) + ... + c(n), where b(n) = A011916(n), c(n) = A011918(n).

12, 1980, 378840, 73419192, 14241916260, 2762844014580, 535977297450672, 103976830083273840, 20170969020163148220, 3913064012542622257452, 759114247456742016195720, 147264250942490855924510760

Offset: 1

Author

Mario Velucchi (mathchess(AT)velucchi.it)

Keywords

• nonn
• easy

References

• Mario Velucchi "Seeing couples" in Recreational and Educational Computing, to appear 1997.

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..437
• Index entries for linear recurrences with constant coefficients, signature (209,-2926,2926,-209,1).

Programs

Maple

A011922 := proc(n) (2+sqrt(1+((((2+sqrt(3))^(2*n)-(2-sqrt(3))^(2*n))^2)/4)))/3 ; expand(%) ; simplify(%) ; end proc:
A011916 := proc(n) ((A011922(n)-1)+sqrt(3*A011922(n)^2-4*A011922(n)+1))/2 ; end proc:
A011920 := proc(n) A011916(n)*(A011916(n)+1) ; end proc:
seq(A011920(n),n=1..20) ; # R. J. Mathar, Apr 15 2010

Mathematica

LinearRecurrence[{209,-2926,2926,-209,1},{12,1980,378840,73419192,14241916260},20] (* Harvey P. Dale, Jan 01 2021 *)

Formula

From R. J. Mathar, Apr 15 2010: (Start)

a(n) = +209*a(n-1) -2926*a(n-2) +2926*a(n-3) -209*a(n-4) +a(n-5).

G.f.: -12*x*(1-44*x+11*x^2)/ ((x-1) * (x^2-14*x+1) * (x^2-194*x+1)). (End)

Extensions

More terms from R. J. Mathar, Apr 15 2010