OFFSET
1,2
COMMENTS
LINKS
FORMULA
a(n) = A001541(n) - 1.
a(n) = (1/2)*(s^n + t^n) - 1, where s = 3 + 2*sqrt(2), t = 3 - 2*sqrt(2). Note: s=1/t. a(n) = 6*a(n-1) - a(n-2) + 4, a(0)=0, a(1)=2.
a(n) = 1/kappa(sqrt(2)/A001542(n)); a(n) = 1/kappa(sqrt(8)/A005319(n)) where kappa(x) is the sum of successive remainders by computing the Euclidean algorithm for (1, x). - Thomas Baruchel, Nov 29 2003
G.f.: -2*x^2*(x+1)/((x-1)*(x^2-6*x+1)). - Colin Barker, Nov 22 2012
MATHEMATICA
a[0] = 0; a[1] = 2; a[n_] := a[n] = 6a[n - 1] - a[n - 2] + 4; Table[ a[n], {n, 0, 20}]
LinearRecurrence[{7, -7, 1}, {0, 2, 16}, 30] (* Harvey P. Dale, Nov 21 2015 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
James R. Buddenhagen, May 15 2003
EXTENSIONS
More terms from Robert G. Wilson v, May 15 2003
STATUS
approved