A076740 a(n) = 2*a(n-1)^2 - a(n-2)^2 with a(0)=0, a(1)=1.

0, 1, 2, 7, 94, 17623, 621131422, 771608486480914039, 1190759312818733806192492198418844958, 2835815482129086304432303489823255992516794878843873643408264712776750007

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..12

Example

a(2) = 2*1^2 - 0^2 = 2 - 0 = 2.
a(3) = 2*2^2 - 1^2 = 8 - 1 = 7.
a(4) = 2*7^2 - 2^2 = 98 - 4 = 94.

Mathematica

a[n_]:= a[n]= If[n<2, n, 2*a[n-1]^2 - a[n-2]^2 ];
Table[a[n], {n, 0, 12}] (* G. C. Greubel, May 02 2022 *)

Prog

(PARI) a=vector(10); a[1]=0; a[2]=1; for (i=3, 10, a[i]=2*a[i-1]^2-a[i-2]^2); a
(SageMath)
def a(n): # a = A076740
    if (n<2): return n
    else: return 2*a(n-1)^2 - a(n-2)^2
[a(n) for n in (0..12)] # G. C. Greubel, May 02 2022

Crossrefs

Sequence in context: A224439 A304722 A056161 * A112290 A072059 A308961

Adjacent sequences: A076737 A076738 A076739 * A076741 A076742 A076743

Keyword

nonn

Author

Jon Perry, Jun 19 2003

Status

approved