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Search: id:A013656
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| 0, 7, 32, 75, 136, 215, 312, 427, 560, 711, 880, 1067, 1272, 1495, 1736, 1995, 2272, 2567, 2880, 3211, 3560, 3927, 4312, 4715, 5136, 5575, 6032, 6507, 7000, 7511, 8040, 8587, 9152, 9735, 10336, 10955, 11592, 12247, 12920, 13611, 14320, 15047, 15792, 16555
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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a(n+1)=A144454(9n+7)=A061039(27n+21),from Paschen spectrum of hydrogen. [From Paul Curtz (bpcrtz(AT)free.fr), Nov 05 2008]
If A=[A013656] 9*n.^2-2*n (n>0, 7, 32, 75,., ,.,); Y=[A010701] 3 (3, 3, 3, ,..,); X=[A017257] 9*n-1 (n>0, 8, 17, 26, 35, ,. .,), we have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 8^2-7 *3^2=1; 17^2-32*3^2=1; 26^2-75*3^2=1. [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 11 2009]
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FORMULA
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a(n)=18*n+a(n-1)-29 (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+0-29=7; n=3, a(3)=18*3+7-29=32; n=4, a(4)=18*4+32-29=75 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 13 2009]
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MATHEMATICA
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s=0; lst={s}; Do[s+=n++ +7; AppendTo[lst, s], {n, 0, 8!, 18}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Nov 16 2008]
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PROGRAM
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(Other) sage: [lucas_number1(3, 3*n, 2*n) for n in xrange(0, 44)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 20 2009]
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CROSSREFS
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Cf. A010701, A017257 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 11 2009]
Sequence in context: A153715 A060123 A013650 this_sequence A067982 A126562 A164270
Adjacent sequences: A013653 A013654 A013655 this_sequence A013657 A013658 A013659
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KEYWORD
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nonn,new
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AUTHOR
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David W. Wilson (davidwwilson(AT)comcast.net)
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