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Search: id:A147296
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| 0, 11, 40, 87, 152, 235, 336, 455, 592, 747, 920, 1111, 1320, 1547, 1792, 2055, 2336, 2635, 2952, 3287, 3640, 4011, 4400, 4807, 5232, 5675, 6136, 6615, 7112, 7627, 8160, 8711, 9280, 9867, 10472, 11095, 11736, 12395, 13072, 13767, 14480, 15211, 15960
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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If A=[A147296] 9*n.^2+2*n (n>0, 11, 40, 87,., ,.,); Y=[A010701] 3 (3, 3, 3, ,..,); X=[A017173] 9*n+1 (n>0, 10, 19, 28, ,. .,), we have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 10^2-11*3^2=1; 19^2-40*3^2=1; 28^2-87*3^2=1. [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 11 2009]
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LINKS
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Reply to V. Librandi, A147296 (SeqFan list) [From M. F. Hasler (MHasler(AT)univ-ag.fr), Mar 01 2009]
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FORMULA
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A147296(n) = n(9n + 2), as conjectured by V. Librandi. [From M. F. Hasler (MHasler(AT)univ-ag.fr), Mar 01 2009]
G.f.: x*(11+7*x)/(1-x)^3 [From Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Aug 30 2009]
a(n)=18*n+a(n-1)-25 (with a(1)=0) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 13 2009]
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EXAMPLE
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For n=2, a(2)=18*2+0-25=11; n=3, a(3)=18*3+11-25=40; n=4, a(4)=18*4+40-25=87 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 13 2009]
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PROGRAM
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(PARI) A147296(n) = n*(9*n + 2) [From M. F. Hasler (MHasler(AT)univ-ag.fr), Mar 01 2009]
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CROSSREFS
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Equals first 9-fold decimation of A144454.
Cf. A010701, A017173 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 11 2009]
Sequence in context: A077568 A122014 A031427 this_sequence A059142 A064798 A056124
Adjacent sequences: A147293 A147294 A147295 this_sequence A147297 A147298 A147299
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KEYWORD
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nonn,new
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AUTHOR
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Paul Curtz (bpcrtz(AT)free.fr), Nov 05 2008
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EXTENSIONS
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Simpler definition from Vincenzo Librandi, Mar 01 2009
More terms from M. F. Hasler (MHasler(AT)univ-ag.fr), Mar 01 2009
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