A105426 a(0)=1, a(1)=5, a(n)=8*a(n-1)-a(n-2).

1, 5, 39, 307, 2417, 19029, 149815, 1179491, 9286113, 73109413, 575589191, 4531604115, 35677243729, 280886345717, 2211413522007, 17410421830339, 137071961120705, 1079165267135301, 8496250175961703, 66890836140558323

Offset: 0

Author

Michael Somos, Apr 10 2005

Keywords

• nonn
• easy

Comments

15*a(n)^2-14 is a square for all n.

Links

• Tanya Khovanova, Recursive Sequences
• Index entries for linear recurrences with constant coefficients, signature (8,-1).
• Index entries for two-way infinite sequences

Crossrefs

Cf. a(n) = A001090(n+1) - 3*A001090(n).

Programs

Mathematica

LinearRecurrence[{8,-1},{1,5},20] (* Harvey P. Dale, Feb 25 2016 *)

PARI

a(n)=subst(19*poltchebi(n)-poltchebi(n-1),x,4)/15

Formula

G.f.: (1-3x)/(1-8x+x^2). a(n)=2*A105045(2*n+1)-1. a(-n)=2*A105045(2*n)-1, if n>0.