0,2

Hypotenuse (z) of Pythagorean triples (x,y,z) with |2x-y|=1.

T. D. Noe, Table of n, a(n) for n=0..100

Index entries for sequences related to linear recurrences with constant coefficients

Tanya Khovanova, Recursive Sequences

G.f.: (1-x)/(1-18*x+x^2). a(n)=18*a(n-1)-a(n-2), n>1. a(0)=1, a(1)=17.

a(n+1)=9*a(n)+4*(5*a(n)^2-1)^0.5 - Richard Choulet (richardchoulet(AT)yahoo.fr), Aug 30 2007, Dec 28 2007

a(n) = ((2+sqrt(5))^(2*n+1)-(2-sqrt(5))^(2*n+1))/(2*sqrt(5)). - Dean Hickerson (dean.hickerson(AT)yahoo.com), Dec 09 2002

a(n) ~ (1/10)*sqrt(5)*(sqrt(5) + 2)^(2*n+1) - Joe Keane (jgk(AT)jgk.org), May 15 2002

For all elements x of the sequence, 5*x^2 - 1 is a square. Lim. n->Inf. a(n)/a(n-1) = 8*phi + 5 = 9 + 4*Sqrt(5) - Gregory V. Richardson (omomom(AT)hotmail.com), Oct 13 2002

Let q(n, x)=sum(i=0, n, x^(n-i)*binomial(2*n-i, i)); then a(n)=q(n, 16). - Benoit Cloitre (benoit7848c(AT)orange.fr), Dec 06 2002

a(n) = 19*a(n-1)- 19*a(n-2) + a(n-3); f(x) = (sqrt(5)/10)*((2+sqrt(5))*(9+4*sqrt(5))^(x-1) - (2-sqrt(5))*(9-4*sqrt(5))^(x-1)) - Antonio A. Olivares (olivares14031(AT)yahoo.com), May 15 2008

a(n) = 17a(n-1) + 17a(n-2) - a(n-3) - Antonio A. Olivares (olivares14031(AT)yahoo.com), Jun 19 2008

a(n)=A001076(2n+1).

Row 18 of array A094954.

Cf. A001076.

Sequence in context: A163049 A083453 A090437 this_sequence A158585 A156085 A129992

Adjacent sequences: A007802 A007803 A007804 this_sequence A007806 A007807 A007808

nonn,nice,easy

James A. Raymond (raymond(AT)unlv.edu), Clark Kimberling (ck6(AT)evansville.edu)

Better description and more terms from Michael Somos