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-1, 5, 23, 53, 95, 149, 215, 293, 383, 485, 599, 725, 863, 1013, 1175, 1349, 1535, 1733, 1943, 2165, 2399, 2645, 2903, 3173, 3455, 3749, 4055, 4373, 4703, 5045, 5399, 5765, 6143, 6533, 6935, 7349, 7775, 8213, 8663, 9125, 9599, 10085, 10583, 11093, 11615
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Also: The numerators in the j=2 column of the array a(i,j) defined in A140825, where the columns j=0 and j=1 are represented by A000012 and A005408. This could be extended to column j=3: 1, -1, 9, 55, 161... The common feature of these sequences derived from a(i,j) is that their j-th differences are constant sequences defined by A091137(j).
a(n) is the set of all k such that 6k+6 is a perfect square [From Gary Detlefs (gdetlefs(AT)aol.com), Mar 04 2010]
The identity (6n^2-1)^2-(9n^2-3)*(2n)^2=1 can be written as a(n+1)^2-A157872(n)*A005843(n+1)^2=1. - Vincenzo Librandi, Feb 05 2012
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REFERENCES
| P. Curtz, Integration .. Centre de Calcul Scientifique de l' Armement,Arcueil, (1969) 28-36.
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index to sequences with linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
| a(n)=2a(n-1)-a(n-2)+12.
First differences: a(n+1)-a(n)=A017593(n). Second differences A071593(n+1)-A071593(n)=12.
G.f.: (1-8*x-5*x^2)/(x-1)^3 [From Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Aug 30 2009]
a(n) = a(n-1) +12n -6. - Vincenzo Librandi, Feb 05 2012
a(n) = 3*a(n-1) -3*a(n-2) +a(n-3). - Vincenzo Librandi, Feb 05 2012
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MATHEMATICA
| LinearRecurrence[{3, -3, 1}, {-1, 5, 23}, 40] (* Vincenzo Librandi, Feb 05 2012
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PROG
| (PARI) a(n)=6*n^2-1 \\ Charles R Greathouse IV, Jun 01 2011
(MAGMA) [6*n^2 - 1: n in [0..50]]; // Vincenzo Librandi, Jun 02 2011
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CROSSREFS
| Cf. A005843, A157872.
Sequence in context: A127200 A147113 A135771 * A090686 A082277 A155851
Adjacent sequences: A140808 A140809 A140810 * A140812 A140813 A140814
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KEYWORD
| sign,easy,changed
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AUTHOR
| Paul Curtz (bpcrtz(AT)free.fr), Jul 16 2008
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EXTENSIONS
| Edited and extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 06 2008
Better description Ray Chandler (rayjchandler(AT)sbcglobal.net), Feb 03 2009
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