0,1

a(n+1)/a(n) converges to (76+sqrt(5780))/2 = 76.01315561749... a(0)/a(1)=2/76; a(1)/a(2)=76/5778; a(2)/a(3)= 5778/439204; a(3)/a(4)= 439204/33385282; ... etc. Lim a(n)/a(n+1) as n approaches infinity = 0.01315561749... = 2/(76+sqrt(5780)) = (sqrt(5780)-76)/2.

Tanya Khovanova, Recursive Sequences

Index entries for recurrences a(n) = k*a(n - 1) +/- a(n - 2)

a(n) =76a(n-1) + a(n-2), starting with a(0) = 2 and a(1) = 76, a(n) = ((76+sqrt(5780))/2)^n + ((76-sqrt(5780))/2)^n, (a(n))^2 =a(2n)-2 if n=1, 3, 5..., (a(n))^2 =a(2n)+2 if n=2, 4, 6....

G.f.: (2-76*x)/(1-76*x-x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 02 2008]

a(4) = 33385282 = 76a(3) + a(2) = 76*439204+ 5778=((76+sqrt(5780))/2)^4 + ( (76-sqrt(5780))/2)^4 =33385281.999999970046 + 0.000000029953 =33385282.

Cf. A000032.

Sequence in context: A116172 A000329 A091978 this_sequence A041721 A048358 A124456

Adjacent sequences: A087284 A087285 A087286 this_sequence A087288 A087289 A087290

easy,nonn

Nikolay V. Kosinov (kosinov(AT)unitron.com.ua), Oct 19 2003