A097705 a(n) = 4*a(n-1) + 17*a(n-2), a(1)=1, a(2)=4.

1, 4, 33, 200, 1361, 8844, 58513, 384400, 2532321, 16664084, 109705793, 722112600, 4753448881, 31289709724, 205967469873, 1355794944800, 8924626767041, 58747021129764, 386706739558753, 2545526317441000

Offset: 1

Author

Ralf Stephan, Aug 27 2004

Keywords

• nonn
• easy

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

• A. Bremner and N. Tzanakis, Lucas sequences whose 8th term is a square
• Index entries for linear recurrences with constant coefficients, signature (4,17).

Crossrefs

Cf. A006131.

Programs

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

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 */

Formula

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

Extensions

Definition adapted to offset by Georg Fischer, Jun 18 2021