Logo

Greetings from The On-Line Encyclopedia of Integer Sequences!

Hints

Search: id:A011944
Displaying 1-1 of 1 results found. page 1
     Format: long | short | internal | text      Sort: relevance | references | number      Highlight: on | off
A011944 a(n) = 14*a(n-1)-a(n-2) with a(0) = 0, a(1) = 2. +0
2
0, 2, 28, 390, 5432, 75658, 1053780, 14677262, 204427888, 2847313170, 39657956492, 552364077718, 7693439131560, 107155783764122, 1492487533566148, 20787669686161950, 289534888072701152 (list; graph; listen)
OFFSET

0,2

COMMENT

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]

a(n)=14*a(n-1)-a(n-2), with a(1)=0, a(2)=2: Example: a(3)=14*a(2)-a(1)=14*2-0=28; a(4)=14*28-2=390; a(5)=14*390-28=5432. [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Feb 16 2009]

CROSSREFS

a(n) = 2 * A007655 = {A001353(2n)}/2. Cf. A011943.

Sequence in context: A092801 A152280 A061629 this_sequence A012745 A143585 A151332

Adjacent sequences: A011941 A011942 A011943 this_sequence A011945 A011946 A011947

KEYWORD

nonn,easy

AUTHOR

E. K. Lloyd

EXTENSIONS

More terms from Gregory V. Richardson (omomom(AT)hotmail.com), Oct 13 2002

page 1

Search completed in 0.002 seconds

Lookup | Welcome | Find friends | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Puzzles | Hot | Classics
More pages | Superseeker | Maintained by N. J. A. Sloane (njas@research.att.com)

Last modified November 25 13:47 EST 2009. Contains 167481 sequences.


AT&T Labs Research