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Search: id:A011944
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| A011944 |
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a(n) = 14*a(n-1)-a(n-2) with a(0) = 0, a(1) = 2. |
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+0
2
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| 0, 2, 28, 390, 5432, 75658, 1053780, 14677262, 204427888, 2847313170, 39657956492, 552364077718, 7693439131560, 107155783764122, 1492487533566148, 20787669686161950, 289534888072701152
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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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
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REFERENCES
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E. K. Lloyd "The standard deviation of 1, 2, .., n, Pell's equation and rational triangles", preprint.
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LINKS
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Index entries for sequences related to linear recurrences with constant coefficients
Tanya Khovanova, Recursive Sequences
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FORMULA
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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]
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CROSSREFS
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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
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KEYWORD
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nonn,easy
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AUTHOR
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E. K. Lloyd
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EXTENSIONS
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More terms from Gregory V. Richardson (omomom(AT)hotmail.com), Oct 13 2002
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