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A097705 a(n) = 4*a(n-1) + 17*a(n-2), a(1)=1, a(2)=4. 2
1, 4, 33, 200, 1361, 8844, 58513, 384400, 2532321, 16664084, 109705793, 722112600, 4753448881, 31289709724, 205967469873, 1355794944800, 8924626767041, 58747021129764, 386706739558753, 2545526317441000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

This is one of only two Lucas-type sequences whose 8th term is a square.

The other one is A006131. - Michel Marcus, Dec 07 2012

LINKS

Table of n, a(n) for n=1..20.

A. Bremner and N. Tzanakis, Lucas sequences whose 8th term is a square

Index entries for linear recurrences with constant coefficients, signature (4,17).

FORMULA

G.f.: 1/(1-4x-17x^2).

a(n)=-(1/42)*[2-sqrt(21)]^n*sqrt(21)+(1/42)*sqrt(21)*[2+sqrt(21)]^n, with n>=0. -Paolo P. Lava, Oct 02 2008

MAPLE

f:= gfun:-rectoproc({a(n) = 4*a(n-1) + 17*a(n-2), a(1)=1, a(2)=4}, a(n), remember): map(f, [$0..20]); # Georg Fischer, Jun 18 2021

PROG

(Maxima)

a[0]:0$

a[1]:1$

a[n]:=4*a[n-1] + 17*a[n-2]$

A097705(n):=a[n]$

makelist(A097705(n), n, 1, 30); /* Martin Ettl, Nov 03 2012 */

CROSSREFS

Cf. A006131.

Sequence in context: A013192 A273700 A273708 * A131509 A221030 A081007

Adjacent sequences:  A097702 A097703 A097704 * A097706 A097707 A097708

KEYWORD

nonn,easy

AUTHOR

Ralf Stephan, Aug 27 2004

EXTENSIONS

Definition adapted to offset by Georg Fischer, Jun 18 2021

STATUS

approved

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Last modified December 3 18:19 EST 2021. Contains 349467 sequences. (Running on oeis4.)