|
| |
|
|
A011944
|
|
a(n) = 14*a(n-1)-a(n-2) with a(0) = 0, a(1) = 2.
|
|
3
|
|
|
|
0, 2, 28, 390, 5432, 75658, 1053780, 14677262, 204427888, 2847313170, 39657956492, 552364077718, 7693439131560, 107155783764122, 1492487533566148, 20787669686161950, 289534888072701152
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
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
|
|
|
LINKS
|
Table of n, a(n) for n=0..16.
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-> Inf. 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 (bhmd95(AT)yahoo.fr), 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). [From Philippe Deléham, Nov 17 2008]
|
|
|
CROSSREFS
|
a(n) = 2 * A007655 = {A001353(2n)}/2. Cf. A011943.
Sequence in context: A152280 A061629 A230130 * A271565 A241365 A240771
Adjacent sequences: A011941 A011942 A011943 * A011945 A011946 A011947
|
|
|
KEYWORD
|
nonn,easy
|
|
|
AUTHOR
|
E. K. Lloyd
|
|
|
STATUS
|
approved
|
| |
|
|
