A011920 - OEIS

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

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OFFSET

1,1

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).

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)

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 *)

CROSSREFS

Sequence in context: A167745 A326601 A265216 * A323817 A263584 A323816

Adjacent sequences: A011917 A011918 A011919 * A011921 A011922 A011923

KEYWORD

nonn,easy

AUTHOR

Mario Velucchi (mathchess(AT)velucchi.it)

EXTENSIONS

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

STATUS

approved