A107706 Quadratic recurrence a(n)=2a(n-1)^2+a(n-2), a(0)=a(1)=1.

1, 1, 3, 19, 725, 1051269, 2210333021447, 9771144131398048324998887, 190950515273109040540985906104397627141067435498985, 72924198566131697919005645563941249133599421947333610081098812005030529313728193495031984760197059337

Offset

0,3

Links

Table of n, a(n) for n=0..9.

Formula

a(n) ~ 1/2 * c^(2^n), where c = 1.5761071725603835806427292143532632951057735784139134374711... . - Vaclav Kotesovec, Jan 19 2015

Mathematica

RecurrenceTable[{a[n]==2*a[n-1]^2+a[n-2], a[0]==1, a[1]==1}, a, {n, 0, 10}] (* Vaclav Kotesovec, Jan 19 2015 *)

Prog

(PARI) a(n)=if(n<0, -a(-1-n), if(n<2, 1, 2*a(n-1)^2+a(n-2)))

Crossrefs

Sequence in context: A272571 A355615 A329470 * A373626 A330040 A168591

Adjacent sequences: A107703 A107704 A107705 * A107707 A107708 A107709

Keyword

nonn

Author

Michael Somos, May 22 2005

Status

approved