OFFSET
0,2
COMMENTS
Standard deviation of A011943.
Product x*y, where the pair (x, y) solves for x^2 - 3y^2 = 1, i.e., a(n)=A001075(n)*A001353(n). - Lekraj Beedassy, Jul 13 2006
Solutions m to the Diophantine equation where square m^2 = k*(k+1)/3, corresponding solutions k are in A007654. - Bernard Schott, Apr 10 2021
All solutions for y in Pell equation x^2 - 12*y^2 = 1. Corresponding values for x are in A011943. - Herbert Kociemba, Jun 05 2022
LINKS
Tanya Khovanova, Recursive Sequences
E. Keith Lloyd, The Standard Deviation of 1, 2,..., n: Pell's Equation and Rational Triangles, Math. Gaz. vol 81 (1997), 231-243.
Index entries for linear recurrences with constant coefficients, signature (14,-1).
FORMULA
For all members x of the sequence, 12*x^2 +1 is a square. Lim_{n->infinity} a(n)/a(n-1) = 7 + sqrt(12). - Gregory V. Richardson, Oct 13 2002
a(n) = ((7+2*sqrt(12))^(n-1) - (7-2*sqrt(12))^(n-1)) / (2*sqrt(12)). - Gregory V. Richardson, Oct 13 2002
a(n) = 13*(a(n-1) + a(n-2)) - a(n-3). a(n) = 15*(a(n-1) - a(n-2)) + a(n-3). - Mohamed Bouhamida, Sep 20 2006
a(n) = sinh(2n*arcsinh(sqrt(3)))/sqrt(12). - Herbert Kociemba, Apr 24 2008
G.f.: 2x/(1-14*x+x^2). - Philippe Deléham, Nov 17 2008
MATHEMATICA
LinearRecurrence[{14, -1}, {0, 2}, 20] (* Harvey P. Dale, Oct 17 2019 *)
Table[2 ChebyshevU[-1 + n, 7], {n, 0, 18}] (* Herbert Kociemba, Jun 05 2022 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
E. K. Lloyd
STATUS
approved