|
| |
|
|
A011944
|
|
a(n) = 14*a(n-1)-a(n-2) with a(0) = 0, a(1) = 2.
|
|
1
| |
|
|
0, 2, 28, 390, 5432, 75658, 1053780, 14677262, 204427888, 2847313170, 39657956492, 552364077718, 7693439131560, 107155783764122, 1492487533566148, 20787669686161950, 289534888072701152
(list; graph; refs; listen; history; 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 (blekraj(AT)yahoo.com), Jul 13 2006
|
|
|
REFERENCES
| E. K. Lloyd "The standard deviation of 1, 2, .., n, Pell's equation and rational triangles", preprint.
|
|
|
LINKS
| Index entries for sequences related to linear recurrences with constant coefficients
Tanya Khovanova, Recursive Sequences
|
|
|
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 (omomom(AT)hotmail.com), Oct 13 2002
a(n) = [(7+2*Sqrt(12))^(n-1) - (7-2*Sqrt(12))^(n-1)] / (2*Sqrt(12)) - Gregory V. Richardson (omomom(AT)hotmail.com), 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 (kociemba(AT)t-online.de), Apr 24 2008
G.f.: 2x/(1-14*x+x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 17 2008]
|
|
|
CROSSREFS
| a(n) = 2 * A007655 = {A001353(2n)}/2. Cf. A011943.
Sequence in context: A092801 A152280 A061629 * A012745 A143585 A151332
Adjacent sequences: A011941 A011942 A011943 * A011945 A011946 A011947
|
|
|
KEYWORD
| nonn,easy
|
|
|
AUTHOR
| E. K. Lloyd
|
|
|
EXTENSIONS
| More terms from Gregory V. Richardson (omomom(AT)hotmail.com), Oct 13 2002
|
| |
|
|
